样式: 排序: IF: - GO 导出 标记为已读
-
A global Morse index theorem and applications to Jacobi fields on CMC surfaces Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-28 Wu-Hsiung Huang
In this paper, we establish a “global” Morse index theorem. Given a hypersurface Mn of constant mean curvature, immersed in ℝn+1. Consider a continuous deformation of “generalized” Lipschitz domain D(t) enlarging in Mn. The topological type of D(t) is permitted to change along t, so that D(t) has an arbitrary shape which can “reach afar” in Mn, i.e. cover any preassigned area. The proof of the global
-
Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-23 Vincenzo Ambrosio
We consider the fractional relativistic Schrödinger–Choquard equation (−Δ+m2)su+V(𝜀x)u=1|x|μ∗F(u)f(u)inℝN,u∈Hs(ℝN),u>0inℝN, where 𝜀>0 is a small parameter, s∈(0,1), m>0, N>2s, μ∈(0,2s), (−Δ+m2)s is the fractional relativistic Schrödinger operator, V:ℝN→ℝ is a continuous potential having a local minimum, f:ℝ→ℝ is a continuous nonlinearity with subcritical growth at infinity and F(t)=∫0tf(τ)dτ. Exploiting
-
Weight module classifications for Bershadsky–Polyakov algebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-23 Dražen Adamović, Kazuya Kawasetsu, David Ridout
The Bershadsky–Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated with 𝔰𝔩3. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys.111 (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov’s
-
Geodesics on adjoint orbits of SL(n, ℝ) Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-23 Brian Grajales, Lino Grama, Rafaela F. Prado
In this paper, we examine the geodesics on adjoint orbits of SL(n,ℝ) that are equipped with SO(n)-invariant metrics, where SO(n) is the maximal compact subgroup. Our primary technique involves translating this problem into a geometric problem in the tangent bundle of certain SO(n)-flag manifolds and describing the geodesic equations with respect to the Sasaki metric on the tangent bundle. Additionally
-
Toroidal extended affine Lie algebras and vertex algebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-23 Fulin Chen, Haisheng Li, Shaobin Tan
In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their ϕ-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and ϕ-coordinated modules
-
Perspective functions with nonlinear scaling Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-19 Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally
-
Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-16 Amin Esfahani, Achenef Tesfahun
In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term Δu in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition
-
On fractional parabolic equations with Hardy-type potentials Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-14 Veronica Felli, Ana Primo, Giovanni Siclari
A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren–Poon monotonicity formula combined with a blow-up analysis.
-
On the cohomology of NC(−2) in positive characteristic Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-14 Eric Larson
Let C⊂ℙ3 be a general Brill–Noether curve. A classical problem is to determine when H0(NC(−2))=0, which controls the quadric section of C. So far this problem has only been solved in characteristic zero, in which case H0(NC(−2))=0 with finitely many exceptions. In this paper, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic 2.
-
The Bernstein problem for (X,Y )-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-09 Gianmarco Giovannardi, Manuel Ritoré
In the Heisenberg group ℍ1 with a sub-Finsler structure, an (X,Y)-Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic graphs of Euclidean Lipschitz functions.
-
Exceptionally simple super-PDE for F(4) Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-02-01 Andrea Santi, Dennis The
For the largest exceptional simple Lie superalgebra F(4), having dimension (24|16), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second- and third-order, respectively.
-
Algebraic versions of Hartogs’ theorem Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-01-29 Marcin Bilski, Jacek Bochnak, Wojciech Kucharz
Let 𝕂 be an uncountable field of characteristic 0. For a given function f:𝕂n→𝕂, with n≥2, we prove that f is regular if and only if the restriction f|C is a regular function for every algebraic curve C in 𝕂n which is either an affine line or is isomorphic to a plane curve in 𝕂2 defined by the equation Xp−Yq=0, where p
-
Curvature of new Kähler metrics on the total space of Griffiths negative vector bundle and quasi-Fuchsian space Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-01-24 Inkang Kim, Xueyuan Wan, Genkai Zhang
We study Kähler metrics on the total space of Griffiths negative holomorphic vector bundles over Kähler manifolds. As an application, we construct mapping class group invariant Kähler metrics on ℬ(𝒮), the holomorphic tangent bundle of Teichmüller space of a closed surface S. Consequently,we obtain a new mapping class group invariant Kähler metric on the quasi-Fuchsian space QF(S), which extends the
-
A comparison principle for a doubly singular quasilinear anisotropic problem Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-01-24 Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta
In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator −ΔpHu:=−div(Hp−1(∇u)∇H(∇u)). As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in
-
Einstein Lie groups, geodesic orbit manifolds and regular Lie subgroups Commun. Contemp. Math. (IF 1.6) Pub Date : 2024-01-24 Nikolaos Panagiotis Souris
We study the relation between two special classes of Riemannian Lie groups G with a left-invariant metric g: The Einstein Lie groups, defined by the condition Ricg=cg, and the geodesic orbit Lie groups, defined by the property that any geodesic is the integral curve of a Killing vector field. The main results imply that extensive classes of compact simple Einstein Lie groups (G,g) are not geodesic
-
Persistent homology for functionals Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-30 Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse
-
Boundary restricted Brunn–Minkowski inequalities Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-30 Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka
In this paper, we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V. Milman regarding the volume of ∂K+∂T where K and T are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of sets with connected boundary, as well as some related results.
-
Convexity of energy functions of harmonic maps homotopic to covering maps of surfaces Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-22 Inkang Kim, Xueyuan Wan, Genkai Zhang
We study the strict convexity of the energy function of harmonic maps at their critical points from a Riemann surface to a Riemann surface, or to the product of negatively curved surfaces. When the target is a Riemann surface and when the map is of nonzero degree, we obtain a precise formula for the second derivative of the energy function along a Weil–Petersson geodesic, which implies that the energy
-
Timelike Ricci bounds for low regularity spacetimes by optimal transport Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-14 Mathias Braun, Matteo Calisti
We prove that a globally hyperbolic smooth spacetime endowed with a C1-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces
-
On the conditional existence of foliations by CMC and Willmore type half-spheres Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-12 Jan-Henrik Metsch
We study half-spheres with small radii λ sitting on the boundary of a smooth bounded domain while meeting it orthogonally. Even though it is known that there exist families of CMC and Willmore type half-spheres near a nondegenerate critical point p of the domains boundaries mean curvature, it is unknown in both cases whether these provide a foliation of any deleted neighborhood of p. We prove that
-
Harmonic maps on locally conformal almost cosymplectic manifolds Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-09 Cătălin Gherghe, Gabriel-Eduard Vîlcu
We investigate harmonic maps on almost contact metric manifolds which are locally conformal to almost cosymplectic manifolds. We obtain the necessary and sufficient conditions for the holomorphy to imply harmonicity and then we find obstructions to the existence of non-constant pluriharmonic maps. We also establish some results on the stability of the identity map on a locally conformal almost cosymplectic
-
Fractional anisotropic Calderón problem on complete Riemannian manifolds Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-09 Mourad Choulli, El Maati Ouhabaz
We prove that the metric tensor g of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator associated with a fractional power of the Laplace–Beltrami operator Δg. Our result holds under the condition that the metric tensor g is known in an arbitrary small subdomain. We also consider the case of closed manifolds and provide an
-
On exponential stability of switched functional differential equations with average dwell-time Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-08 Pham Huu Anh Ngoc, Le Trung Hieu, Thai Bao Tran
We present a novel approach to the exponential stability of switched functional differential equations. Our approach does not involve Lyapunov functions. It is simple and based upon spectral properties of Metzler matrices, a comparison principle and the average dwell-time technique. Consequently, some new explicit criteria for the exponential stability of switched functional differential equations
-
Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-12-02 Jun Hu, Lei Shi
In this paper we give a closed formula for the graded dimension of the cyclotomic quiver Hecke algebra ℛΛ(β) associated to an arbitrary symmetrizable Cartan matrix A=(aij)i,j∈I, where Λ∈P+ and β∈Qn+. As applications, we obtain some necessary and sufficient conditions for the KLR idempotent e(ν) (for any ν∈Iβ) to be nonzero in the cyclotomic quiver Hecke algebra ℛΛ(β). We prove several level reduction
-
A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie Poisson bialgebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-29 Guilai Liu, Chengming Bai
The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2-cocycles on the Lie algebras instead. Explicitly, we first introduce
-
Prime ideals in infinite products of commutative rings Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-27 Carmelo A. Finocchiaro, Sophie Frisch, Daniel Windisch
We describe the prime ideals and, in particular, the maximal ideals in products R=∏Dλ of families (Dλ)λ∈Λ of commutative rings. We show that every maximal ideal is induced by an ultrafilter on the Boolean algebra ∏𝒫(max(Dλ)), where max(Dλ) is the spectrum of maximal ideals of Dλ, and 𝒫 denotes the power set. If every Dλ is in a certain class of rings including finite character domains and one-dimensional
-
Brezis–Seeger–Van Schaftingen–Yung-type characterization of homogeneous ball Banach Sobolev spaces and its applications Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-24 Chenfeng Zhu, Dachun Yang, Wen Yuan
Let γ∈ℝ∖{0} and X(ℝn) be a ball Banach function space satisfying some extra mild assumptions. Assume that Ω=ℝn or Ω⊂ℝn is an (𝜀,∞)-domain for some 𝜀∈(0,1]. In this paper, the authors prove that a function f belongs to the homogeneous ball Banach Sobolev space Ẇ1,X(Ω) if and only if f∈Lloc1(Ω) and supλ∈(0,∞)λ∫{y∈Ω: |f(⋅)−f(y)|>λ|⋅−y|1+γp}⋅−yγ−ndy1pX(Ω)<∞, where p∈[1,∞) is related to X(ℝn). This result
-
The moment map for the variety of Leibniz algebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-15 Zhiqi Chen, Saiyu Wang, Hui Zhang
We consider the moment map m:ℙVn→i𝔲(n) for the action of GL(n) on Vn=⊗2(ℂn)∗⊗ℂn, and study the functional Fn=∥m∥2 restricted to the projectivizations of the algebraic varieties of all n-dimensional Leibniz algebras Ln and all n-dimensional symmetric Leibniz algebras Sn, respectively. First, we give a description of the maxima and minima of the functional Fn:Ln→ℝ, proving that they are actually attained
-
Global classical solutions for three-dimensional compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in bounded domains Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-15 Yang Liu, Xin Zhong
In this paper, we study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total
-
Fast-reaction limit of reaction–diffusion systems with nonlinear diffusion Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-10 Elaine Crooks, Yini Du
In this paper, we present an approach to characterizing fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction–diffusion equations, or one reaction–diffusion equation and one ordinary differential equation, on unbounded domains. Here, we replace the terms of the form uxx in usual reaction–diffusion equation, which represent linear diffusion, by terms of form ϕ(u)xx
-
Properties of gradient maps associated with action of real reductive group Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-11-08 L. Biliotti, Oluwagbenga Joshua Windare
Let (Z,ω) be a Kähler manifold and let U be a compact connected Lie group with Lie algebra 𝔲 acting on Z and preserving ω. We assume that the U-action extends holomorphically to an action of the complexified group Uℂ and the U-action on Z is Hamiltonian. Then there exists a U-equivariant momentum map μ:Z→𝔲. If G⊂Uℂ is a closed subgroup such that the Cartan decomposition Uℂ=Uexp(i𝔲) induces a Cartan
-
Associative algebras and the representation theory of grading-restricted vertex algebras Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-10-06 Yi-Zhi Huang
We introduce an associative algebra A∞(V) using infinite matrices with entries in a grading-restricted vertex algebra V such that the associated graded space Gr(W)=∐n∈ℕGrn(W) of a filtration of a lower-bounded generalized V-module W is an A∞(V)-module satisfying additional properties (called a nondegenerate graded A∞(V)-module). We prove that a lower-bounded generalized V-module W is irreducible or
-
A Steklov version of the torsional rigidity Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-29 L. Brasco, M. González, M. Ispizua
Motivated by the connection between the first eigenvalue of the Dirichlet–Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathematically interesting new concept for boundary torsional rigidity, closely related to the Steklov eigenvalue. From a variational point of view, such a new object corresponds to the sharp constant for the trace embedding of W1
-
Almost sharp weighted Sobolev trace inequalities in the unit ball under constraints Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-20 Jiaxing An, Jingbo Dou, Yazhou Han
In this paper, we establish some improved weighted Sobolev trace inequalities H1(ρ1−2σ,𝔹n+1)↪Lq(𝕊n) under the zero higher order moments constraint via the concentration compactness principle, where ρ is a defining function of 𝔹n+1 and σ∈(0,1). This relates to the fractional (conformal) Laplacians and related problems in conformal geometry. We construct some test functions and show that the inequality
-
Solvability of the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with variable viscosity coefficient Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-20 Zihui He, Xian Liao
We show the existence and the regularity properties of (a class of) weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with density-dependent viscosity coefficients, by analyzing a fourth-order nonlinear elliptic equation for the stream function. For some stationary symmetric flows, we reformulate the Navier–Stokes equations as ordinary differential
-
A causal characterization of Spell+(2n) Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-15 Jakob Hedicke
We show that the natural bi-invariant cone structure on the linear symplectic group Sp(2n) is globally hyperbolic in the positively elliptic region Spell+(2n). This answers a question by Abbondandolo, Benedetti and Polterovich and implies a formula for a bi-invariant Lorentzian distance function defined by these authors for elements in this region. Moreover we give a characterization of the positively
-
A geometric approach to the modified Milnor problem Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-13 Lina Chen, Xiaochun Rong, Shicheng Xu
The Milnor Problem (modified) in the theory of group growth asks whether any finite presented group of vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to the Milnor Problem (modified) is equivalent to the Nilpotency conjecture in Riemannian geometry: given n,d>0, there exists a constant 𝜖(n,d)>0 such that if a compact Riemannian n-manifold M satisfies that
-
The d-critical structure on the Quot scheme of points of a Calabi–Yau 3-fold Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-09-05 Andrea T. Ricolfi, Michail Savvas
The Artin stack ℳn of zero-dimensional sheaves of length n on 𝔸3 carries two natural d-critical structures in the sense of Joyce. One comes from its description as a quotient stack [crit(fn)/GLn], another comes from derived deformation theory of sheaves. We show that these d-critical structures agree. We use this result to prove the analogous statement for the Quot scheme of points Quot𝔸3(𝒪⊕r,n)=crit(fr
-
Generalized Willmore energies, Q-curvatures, extrinsic Paneitz operators, and extrinsic Laplacian powers Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-08-24 Samuel Blitz, A. Rod Gover, Andrew Waldron
Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally invariant differential operator, intrinsically defined on a conformal manifold, mapping scalars to scalars. This operator is a special case of the so-termed extrinsic Paneitz operator defined in the case when the conformal manifold is itself a conformally embedded hypersurface. In particular
-
Behavior of the Poincaré constant along the Polchinski renormalization flow Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-08-17 Jordan Serres
We control the behavior of the Poincaré constant along the Polchinski renormalization flow using a dynamic version of Γ-calculus. We also treat the case of higher order eigenvalues. Our method generalizes a method introduced by Klartag and Putterman to analyze the evolution of log-concave distributions along the heat flow. Furthermore, we apply it to general φ4-measures and discuss the interpretation
-
Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-08-11 Miguel Ballesteros, Gerardo Franco Córdova, Ivan Naumkin, Hermann Schulz-Baldes
This paper proves new results on spectral and scattering theory for matrix-valued Schrödinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson theorem is proved, in which a relation between scattering data and spectral properties (bound and half-bound states) of the corresponding Hamiltonians is derived. The
-
Unboundedness phenomenon in a model of urban crime Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-29 Mario Fuest, Frederic Heihoff
We show that spatial patterns (“hotspots”) may form in the crime model ut=1𝜀Δu−χ𝜀∇⋅uv∇v−𝜀uv,vt=Δv−v+uv, which we consider in Ω=BR(0)⊂ℝn, R>0, n≥3 with 𝜀>0, χ>0 and initial data u0, v0 with sufficiently large initial mass m:=∫Ωu0. More precisely, for each T>0 and fixed Ω, χ and (large) m, we construct initial data v0 exhibiting the following unboundedness phenomenon: Given any M>0, we can find 𝜀>0
-
Degenerations of spherical subalgebras and spherical roots Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-26 Roman Avdeev
In this paper, we obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain one-parameter degenerations of the Lie algebras corresponding to such subgroups. As an application, we exhibit explicit algorithms for computing the set of spherical
-
Steiner and tube formulae in 3D contact sub-Riemannian geometry Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-26 Davide Barilari, Tania Bossio
We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature. It can thus be applied to any surface in a region not containing characteristic points. We provide a geometrical interpretation of the coefficients appearing
-
Non-vanishing higher derived limits Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-20 Boban Veličković, Alessandro Vignati
In the study of strong homology Mardešić and Prasolov isolated a certain inverse system of abelian groups A indexed by elements of ωω. They showed that if strong homology is additive on a class of spaces containing closed subsets of Euclidean spaces then the higher derived limits limnA must vanish, for n>0. They also proved that under the Continuum Hypothesis lim1A≠0. The question whether limnA vanishes
-
Prescribed blow-up sets for sequences of solutions to a non-local Q-curvature equation in ℝ3 Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-20 Yamin Wang
Let Ω⊂ℝ3 be an open connected domain and Δ stand for the Laplacian in ℝ3. For a uniformly bounded sequence (Qk)⊂L∞(Ω) having a fixed sign and non-positive bi-harmonic functions Φ(x,t)∈C∞(ℝ+4∪Ω), we prove that there exists a sequence of solutions (uk) to (−Δ)3/2uk=Qke3ukon Ω,∫Ωe3ukdx<∞, with a total curvature ∫Ω|Qk|e3ukdx=Λ∈(0,∞) such that limk→∞uk(x)=+∞ for x∈S0 and limk→∞uk(x)=−∞ for x∈Ω∖S0, where
-
Averaging for the 2d dispersion-managed NLS Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-07-19 Luccas Campos, Jason Murphy, Tim Van Hoose
We establish global-in-time averaging for the L2-critical dispersion-managed nonlinear Schrödinger equation in the fast dispersion management regime. In particular, in the case of nonzero average dispersion, we establish averaging with any subcritical data, while in the case of a strictly positive dispersion map, we obtain averaging for data in L2.
-
A Blaschke–Lebesgue theorem for the Cheeger constant Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-23 Antoine Henrot, Ilaria Lucardesi
In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible perspective, we conjecture that this maximal property
-
Quantitative quermassintegral inequalities for nearly spherical sets Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-23 Caroline VanBlargan, Yi Wang
In this paper, we establish quantitative Alexandrov–Fenchel inequalities for quermassintegrals on nearly spherical sets. In particular, we bound the (k,m)-isoperimetric deficit from below by the Fraenkel asymmetry. We also find a lower bound on the (k,m)-isoperimetric deficit using the spherical deviation.
-
Self-similar shrinking of supports and non-extinction for a nonlinear diffusion equation with spatially inhomogeneous strong absorption Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-23 Razvan Gabriel Iagar, Philippe Laurençot, Ariel Sánchez
We study the dynamics of the following porous medium equation with strong absorption ∂tu=Δum−|x|σuq, posed for (t,x)∈(0,∞)×ℝN, with m>1, q∈(0,1) and σ>2(1−q)/(m−1). Considering the Cauchy problem with non-negative initial condition u0∈L∞(ℝN), instantaneous shrinking and localization of supports for the solution u(t) at any t>0 are established. With the help of this property, existence and uniqueness
-
The Anzellotti–Gauss–Green formula and least gradient functions in metric measure spaces Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-15 Wojciech Górny, J. M. Mazón
In the framework of the first-order differential structure introduced by Gigli, we obtain a Gauss–Green formula on regular bounded open sets in doubling metric measure spaces supporting a weak Poincaré inequality, valid for BV functions and vector fields with integrable divergence. Then, we study least gradient functions in metric measure spaces and provide an Euler–Lagrange-type formulation of the
-
Analytical solutions to the pressureless Navier–Stokes equations with density-dependent viscosity coefficients Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-09 Jianwei Dong, Hongxia Xue, Qiao Zhang
In this paper, we construct a class of spherically symmetric and self-similar analytical solutions to the pressureless Navier–Stokes equations with density-dependent viscosity coefficients satisfying h(ρ)=ρ𝜃, g(ρ)=(𝜃−1)ρ𝜃 for all 𝜃>0. Under the continuous density free boundary conditions imposed on the free surface, we investigate the large-time behavior of the solutions according to various 𝜃>1
-
On the rigidity of self-shrinkers of the r-mean curvature flow Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-09 Márcio Batista, Wagner Xavier
In this paper, we consider self-similar solutions of the r-mean curvature flow into the (n+1)-dimensional Euclidean space. By employing some general maximum principles as the main tool, we characterize some self-similar solutions of the r-mean curvature flow under some suitable geometric constraints.
-
Continuous time approximation of Nash equilibria in monotone games Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-06-06 Romeo Awi, Ryan Hynd, Henok Mawi
We consider the problem of approximating Nash equilibria of N functions f1,…,fN of N variables. In particular, we show systems of the form u̇j(t)=−∇xjfj(u(t))(j=1,…,N) are well-posed and the large time limits of their solutions u(t)=(u1(t),…,uN(t)) are Nash equilibria for f1,…,fN provided that these functions satisfy an appropriate monotonicity condition. To this end, we will invoke the theory of maximal
-
Incidence varieties in the projectivized kth Hodge bundle over curves with rational tails Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-25 Iulia Gheorghita, Nicola Tarasca
Over the moduli space of pointed smooth algebraic curves, the projectivized kth Hodge bundle is the space of k-canonical divisors. The incidence loci are defined by requiring the k-canonical divisors to have prescribed multiplicities at the marked points. We compute the classes of the closure of the incidence loci in the projectivized kth Hodge bundle over the moduli space of curves with rational tails
-
Undecidably semilocalizable metric measure spaces Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-23 Thierry De Pauw
We characterize measure spaces such that the canonical map L∞→L1∗ is surjective. In case of d-dimensional Hausdorff measure on a complete separable metric space X, we give two equivalent conditions. We give examples of X and d so that whether these conditions are met is undecidable in ZFC, including one with d equals the Hausdorff dimension of X.
-
Real order total variation with applications to the loss functions in learning schemes Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-23 Pan Liu, Xin Yang Lu, Kunlun He
Loss functions are an essential part in modern data-driven approaches, such as bi-level training scheme and machine learnings. In this paper, we propose a loss function consisting of a r-order (an)-isotropic total variation semi-norms TVr, r∈ℝ+, defined via the Riemann–Liouville (RL) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness
-
On the optimal Lq-regularity for viscous Hamilton–Jacobi equations with subquadratic growth in the gradient Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-20 Alessandro Goffi
This paper studies a maximal Lq-regularity property for nonlinear elliptic equations of second order with a zeroth order term and gradient nonlinearities having superlinear and subquadratic growth, complemented with Dirichlet boundary conditions. The approach is based on the combination of linear elliptic regularity theory and interpolation inequalities, so that the analysis of the maximal regularity
-
Pinwheels as Lagrangian barriers Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-17 Joé Brendel, Felix Schlenk
The complex projective plane ℂP2 contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation, see for example [J. Evans and I. Smith, Markov numbers and Lagrangian cell complexes in the complex projective plane, Geom. Topol.22 (2018) 1143–1180]. We compute the Gromov width of the complement of pinwheels and show that
-
The Gálvez-Carrillo–Kock–Tonks conjecture for locally discrete decomposition spaces Commun. Contemp. Math. (IF 1.6) Pub Date : 2023-05-15 Wilson Forero
Gálvez-Carrillo et al. [Decomposition spaces, incidence algebras and Möbius inversion III: The decomposition space of Möbius intervals, Adv. Math.334 (2018) 544–584] constructed a decomposition space U of all Möbius intervals, as a recipient of Lawvere’s interval construction for Möbius categories, and conjectured that U enjoys a certain universal property: for every Möbius decomposition space X, the