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Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-06-21 Antonia Jabbour, Stéphane Sabourau
We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are expressed in terms of the area of the punctured sphere. In both cases, we describe the extremal metrics, which are modeled on the Calabi–Croke sphere or the tetrahedral
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Mean convex properly embedded $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$ Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-05-17 Antonio Martínez, Antonio Luis Martínez-Triviño, João Paulo dos Santos
We establish curvature estimates and a convexity result for mean convex properly embedded $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$, i.e., $\varphi$-minimal surfaces when $\varphi$ depends only on the third coordinate of $\mathbb{R}^3$. Led by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana for stable
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Poincaré series of multiplier and test ideals Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-29 Josep Àlvarez Montaner,Luis Núñez-Betancourt
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An upper bound on the hot spots constant Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-29 Stefan Steinerberger
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Mean field equations and domains of first kind Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-29 Daniele Bartolucci, Andrea Malchiodi
In this paper, we are interested in understanding the structure of domains of first and second kind, a concept motivated by problems in statistical mechanics and mean field equations. We prove some openness property for domains of first kind with respect to a suitable topology, as well as some sufficient condition, in terms of the Fourier coefficients of the Riemann map, for a simply connected domain
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Holomorphic semigroups and Sarason’s characterization of vanishing mean oscillation Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-27 Nikolaos Chalmoukis,Vassilis Daskalogiannis
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Curvature estimates for $p$-convex hypersurfaces of prescribed curvature Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-06 Weisong Dong
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On secant defectiveness and identifiability of Segre–Veronese varieties Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-04-05 Antonio Laface,Alex Massarenti,Rick Rischter
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Growth in Chevalley groups relatively to parabolic subgroups and some applications Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-03-28 Ilya D. Shkredov
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Nonsymplectic automorphisms of prime order on O’Grady’s sixfolds Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-03-28 Annalisa Grossi
We classify nonsymplectic automorphisms of prime order on irreducible holomorphic symplectic manifolds of O’Grady’s 6-dimensional deformation type. More precisely, we give a classification of the invariant and coinvariant sublattices of the second integral cohomology group.
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Generalized Gaussian bounds for discrete convolution powers Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-03-22 Jean-François Coulombel,Grégory Faye
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Soliton solutions to the curve shortening flow on the 2-dimensional hyperbolic space Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-03-21 Fábio Nunes da Silva,Keti Tenenblat
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The planar low temperature Coulomb gas: separation and equidistribution Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-28 Yacin Ameur,José Luis Romero
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Geometry and holonomy of indecomposable cones Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-25 Dmitri Alekseevsky,Vicente Cortés,Thomas Leistner
We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non irreducible cones. The latter admit a parallel distribution of null $k$-planes, and we study the cases $k=1$ and $k=2$ in detail
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Whitney’s extension theorem and the finiteness principle for curves in the Heisenberg group Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-14 Scott Zimmerman
Consider the sub-Riemannian Heisenberg group H. In this paper, we answer the following question: given a compact set K ⊆ R and a continuous map f : K → H, when is there a horizontal C curve F : R → H such that F |K = f? Whitney originally answered this question for real valued mappings [35], and Fefferman provided a complete answer for real valued functions defined on subsets of R [12]. We also prove
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Threshold solutions for the nonlinear Schrödinger equation Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-08 Luccas Campos,Luiz Gustavo Farah,Svetlana Roudenko
We study the focusing NLS equation in $\mathbb{R}^N$ in the mass-supercritical and energy-subcritical (or intercritical) regime, with $H^1$ data at the mass-energy threshold $ \mathcal{ME}(u_0)=\mathcal{ME}(Q)$, where $Q$ is the ground state. Previously, Duyckaerts-Merle studied the behavior of threshold solutions in the $H^1$-critical case, in dimensions $N = 3, 4, 5$, later generalized by Li-Zhang
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Decoupling for two quadratic forms in three variables: a complete characterization Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-08 Shaoming Guo,Changkeun Oh,Joris Roos,Po-Lam Yung,Pavel Zorin-Kranich
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Erratum to “Harmonic quasiconformal mappings between $\mathcal{C}^1$ smooth Jordan domains” Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-02-07 David Kalaj
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Quasi-regular Sasakian and K-contact structures on Smale–Barden manifolds Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-25 Alejandro Cañas, Vicente Muñoz, Matthias Schütt, Aleksy Tralle
Smale–Barden manifolds are simply-connected closed $5$-manifolds. It is an important and difficult question to decide when a Smale–Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Kollár)
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A general notion of coherent systems Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-24 Alexander H.W. Schmitt
We look at coherent systems for decorated vector bundles and propose a notion of semistability. In the special case of tensor powers, we will study this notion more closely by doing some non-trivial constructions and computations in geometric invariant theory. It is an interesting aspect that ampleness of the linearization in the geometric invariant theory construction yields a bound on the stability
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On the core of a low dimensional set-valued mapping Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-18 Pavel Shvartsman
LetM = (M, ρ) be a metric space and let X be a Banach space. Let F be a setvalued mapping fromM into the family Km(X) of all compact convex subsets of X of dimension at most m. The main result in our recent joint paper [16] with Charles Fefferman (which is referred to as a “Finiteness Principle for Lipschitz selections”) provides efficient conditions for the existence of a Lipschitz selection of F
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On profinite groups with positive rank gradient Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-18 Nikolay Nikolov
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Fully nonlinear singularly perturbed models with non-homogeneous degeneracy Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-17 Elzon C. Bezerra Júnior,João Vítor da Silva,Gleydson C. Ricarte
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Stability estimates in inverse problems for the Schrödinger and wave equations with trapping Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-03 Víctor Arnaiz,Colin Guillarmou
For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish Hölder type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schrödinger equation and the wave equation. The novelty in this result lies in the
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Minimal Mahler measures for generators of some fields Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-03 Artūras Dubickas
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Optimal measures for $p$-frame energies on spheres Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2022-01-03 Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the $p$-frame energies, i.e., energies with the kernel given by the absolute value of the inner product raised to a positive power $p$. Application of linear programming methods in the setting of projective spaces allows for describing the minimizing measures
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Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-23 Olivier Le Gal,Mickaël Matusinski,Fernando Sanz Sánchez
We introduce a notion of regular separation for solutions of systems of ODEs $y'=F(x, y)$, where $F$ is definable in a polynomially bounded o-minimal structure and $y= (y_1, y_2)$. Given a pair of solutions with flat contact, we prove that, if one of them has the property of regular separation, the pair is either interlaced or generates a Hardy field. We adapt this result to trajectories of three-dimensional
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Strichartz estimates with broken symmetries Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-20 Felipe Gonçalves,Don B. Zagier
In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr\"{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe an alternative method that is applicable to a wider class of matrix problems.
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Non-symplectic automorphisms of K3 surfaces with one-dimensional moduli space Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-20 Michela Artebani, Paola Comparin, María Elisa Valdés
The moduli space of K3 surfaces $X$ with a purely non-symplectic automorphism $\sigma$ of order $n\geq 2$ is one dimensional exactly when $\varphi(n)=8$ or $10$. In this paper we classify and give explicit equations for the very general members $(X,\sigma)$ of the irreducible components of maximal dimension of such moduli spaces. In particular, we show that there is a unique one-dimensional component
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On digits of Mersenne numbers Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-15 Bryce Kerr,László Mérai,Igor Shparlinski
Motivated by recently developed interest to the distribution of $g$-ary digits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimate rational exponential sums with $M_p$, $p \le X$, modulo a large power of a fixed odd prime $q$. In turn this immediately implies the normality of strings of $q$-ary digits amongst about $(\log X)^{3/2+o(1)}$ rightmost digits of $M_p$, $p \le X$. Previous
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A non-local inverse problem with boundary response Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-15 Tuhin Ghosh
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Extrapolation of compactness on weighted spaces Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-14 Tuomas Hytönen,Stefanos Lappas
Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}$. Then $T$ is bounded and compact on $L^p(w)$ for all $p\in(1,\infty)$ and all $w\in A_p$. This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from a combination of
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Distribution symmetry of toral eigenfunctions Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-13 Ángel D. Martínez, Francisco Torres de Lizaur
In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus, we observe that the symmetry conjecture holds in the strongest possible sense. On the other hand, we provide a counterexample for higher dimensional tori, which relies on a computer-assisted argument. Moreover we prove a theorem on the distribution symmetry of a
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Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-13 Matteo Bordignon
In this paper we obtain a new fully explicit constant for the Pólya–Vinogradov inequality for primitive characters. Given a primitive character $\chi$ modulo $q$, we prove the following upper bound: $$ \Big| \sum_{1 \le n\le N} \chi(n) \Big|\le c \sqrt{q} \log q, $$ where $c=3/(4\pi^2)+o_q(1)$ for even characters and $c=3/(8\pi)+o_q(1)$ for odd characters, with explicit $o_q(1)$ terms. This improves
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Asymptotic convergence of evolving hypersurfaces Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-03 Carlo Mantegazza,Marco Pozzetta
If ψ : M → R is a smooth immersed closed hypersurface, we consider the functional Fm(ψ) = ∫ M 1 + |∇ν| dμ, where ν is a local unit normal vector along ψ, ∇ is the Levi–Civita connection of the Riemannian manifold (M, g), with g the pull–back metric induced by the immersion and μ the associated volume measure. We prove that if m > ⌊n/2⌋ then the unique globally defined smooth solution to the L–gradient
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An example concerning Fourier analytic criteria for translational tiling Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-03 Nir Lev
It is well-known that the functions $f \in L^1(\mathbb{R}^d)$ whose translates along a lattice $\Lambda$ form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a discrete set $\Lambda \subset \mathbb{R}$ (a small perturbation of the integers) for which no characterization of this kind is possible: there are two functions $f, g
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Closed $G_2$-eigenforms and exact $G_2$-structures Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-03 Marco Freibert,Simon Salamon
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Cauchy’s surface area formula in the Heisenberg groups Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-03 Yen-Chang Huang
We show the analogy of Cauchy's surface area formula for the Heisenberg groups $\mathbb{H}_n$ for $n\geq 1$, which states that the p-area of any compact hypersurface $\Sigma$ in $\mathbb{H}_n$ with its p-normal vector defined almost everywhere on $\Sigma$ is the average of its projected p-areas onto the orthogonal complements of all p-normal vectors of the Pansu spheres (up to a constant). The formula
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SDEs with random and irregular coefficients Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-12-03 Guohuan Zhao
We consider Itô uniformly nondegenerate equations with random coefficients. When the coefficients satisfy some low regularity assumptions with respect to the spatial variables and Malliavin differentiability assumptions on the sample points, the unique solvability of singular SDEs is proved by solving backward stochastic Kolmogorov equations and utilizing a modified Zvonkin type transformation.
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Hypercontractivity on the unit circle for ultraspherical measures: linear case Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-15 Paata Ivanisvili, Alexander Lindenberger, Paul F. X. Müller, Michael Schmuckenschläger
In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $\mathbb{R}^n$ and determine best constants. Furthermore, we provide the link to log-Sobolev inequalities and hypercontractivity estimates for ultraspherical measures.
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Variation of the uncentered maximal characteristic function Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-15 Julian Weigt
Let $\mathrm{M}$ be the uncentered Hardy–Littlewood maximal operator, or the dyadic maximal operator, and let $d\geq 1$. We prove that for a set $E\subset\mathbb{R}^d$ of finite perimeter, the bound $\operatorname{var}\mathrm{M} 1_E\leq C_d \operatorname{var} 1_E$ holds. We also prove this for the local maximal operator.
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Uniform energy distribution in a pattern-forming system of surface charges Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-09 Katarina Bellova, Antoine Julia, Felix Otto
We consider a variational model for a charge density $u\in\{-1,1\}$ on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion coming from the electrostatic energy. This competition leads to pattern formation. We prove that the interfacial energy density is (asymptotically) equidistributed at scales large compared to the scale of the pattern. We follow
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Noncommutative partially convex rational functions Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-03 Michael Jury, Igor Klep, Mark E. Mancuso, Scott McCullough, James Eldred Pascoe
Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially convex admit novel butterfly-type realizations that necessitate square roots. A strengthening of partial convexity arising in connection with BMIs – $xy$-convexity
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Restriction estimates for hyperbolic paraboloids in higher dimensions via bilinear estimates Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-02 Alex Barron
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Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-01 Paul Creutz
Our main result gives an improved bound on the filling areas of curves in Banach spaces which are not closed geodesics. As applications we show rigidity of Pu’s classical systolic inequality and investigate the isoperimetric constants of normed spaces. The latter has further applications concerning the regularity of minimal surfaces in Finsler manifolds.
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A construction of equivariant bundles on the space of symmetric forms Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-11-01 Ada Boralevi, Daniele Faenzi, Paolo Lella
We construct stable vector bundles on the space $\mathbb{P}(S^d \mathbb{C}^{n+1})$ of symmetric forms of degree $d$ in $n+1$ variables which are equivariant for the action of $\text{SL}_{n+1}(\mathbb{C})$ and admit an equivariant free resolution of length $2$. For $n=1$, we obtain new examples of stable vector bundles of rank $d-1$ on $\mathbb{P}^d$, which are moreover equivariant for $\operatorna
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A spectral characterization and an approximation scheme for the Hessian eigenvalue Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-10-25 Nam Q. Le
We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear second-order elliptic operators whose coefficients belong to the dual of the corresponding Garding cone. Second, we introduce a non-degenerate inverse iterative scheme
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On BV functions and essentially bounded divergence-measure fields in metric spaces Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-10-12 Vito Buffa, Giovanni E. Comi, Michele Miranda Jr.
By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation (BV) in terms of suitable vector fields on a complete and separable metric measure space $(\mathbb{X},d,\mu)$ equipped with a non-negative Radon measure $\mu$ finite on bounded sets. Then, we extend the concept of divergence-measure vector fields $\mathcal{DM}^p(\mathbb{X})$
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Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operators Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-09-20 Omar EL-Fallah,Mohamed El Ibbaoui
Abstract. Let Ω be a subdomain of C and let μ be a positive Borel measure on Ω. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator Tμ acting on Bergman spaces on Ω. Let (λn(Tμ)) be the decreasing sequence of the eigenvalues of Tμ and let ρ be an increasing function such that ρ(n)/n A is decreasing for some A > 0. We give an explicit necessary and sufficient
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Uniform Sobolev estimates on compact manifolds involving singular potentials Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-09-06 Matthew D. Blair, Xiaoqi Huang, Yannick Sire, Christopher D. Sogge
We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and the fourth author (1986) for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo (2014) for compact Riemannian manifolds involving critically singular potentials $V\in L^{n/2}$. We also obtain the analogous improved quasimode estimates of the first, third and fourth author (2021), Hassell and Tacy (2015), the first
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Hypersurfaces with prescribed curvatures in the de Sitter space Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-17 Ángela Roldán
In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space $\mathbb{S}_1^{n+1}$ and conformal metrics on the sphere $\mathbb{S}^n$. As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in $\mathbb{S}_1^{n+1}$ satisfying certain global conditions and a very general Weingarten relation $W(k_1,\ldots,k_n)
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Cones, rectifiability, and singular integral operators Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-10 Damian Dąbrowski
Let $\mu$ be a Radon measure on $\mathbb{R}^d$. We define and study conical energies $\mathcal{E}_{\mu,p}(x,V,\alpha)$, which quantify the portion of $\mu$ lying in the cone with vertex $x\in\mathbb{R}^d$, direction $V\in G(d,d-n)$, and aperture $\alpha\in (0,1)$. We use these energies to characterize rectifiability and the big pieces of Lipschitz graphs property. Furthermore, if we assume that $\mu$
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On a problem by Nathan Jacobson Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-02 Victor Hugo López Solís, Ivan P. Shestakov
We prove a coordinatization theorem for unital alternative algebras containing $2\times 2$ matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on the description of alternative algebras containing a generalized quaternion algebra $\mathbb{H}$ with the same 1, for the case when the algebra $\mathbb{H}$ is split. In particular, this is the case when
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Oscillating spectral multipliers on groups of Heisenberg type Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-02 Roberto Bramati,Paolo Ciatti,John Green,James Wright
We establish endpoint estimates for a class of oscillating spectral multipliers on Lie groups of Heisenberg type. The analysis follows an earlier argument due to the second and fourth author but requires the detailed analysis of the wave equation on these groups due to Muller and Seeger. We highlight and develop the connection between sharp bounds for oscillating multipliers and the problem of determining
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Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-02 Yong Liu, Juncheng Wei
The elliptic sine-Gordon equation is a semilinear elliptic equation with a special double well potential. It has a family of explicit multiple-end solutions. We show that all finite Morse index solutions belong to this family. It will also be proved that these solutions are nondegenerate, in the sense that the corresponding linearized operators have no nontrivial bounded kernel. Finally, we prove that
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Scattering for critical radial Neumann waves outside a ball Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-08-02 Thomas Duyckaerts, David Lafontaine
We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a nonlinear wave equation with Neumann boundary conditions. Our proof uses the scheme of concentration-compactness/rigidity introduced by Kenig and Merle, extending
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Homology versus homotopy in rational fibrations Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-07-26 Manuel Amann
Motivated by prominent problems like the Hilali conjecture, Yamaguchi– Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rational cohomology groups of fibre, base and total spaces in a fibration of rationally elliptic spaces. In this article we prove these estimates in the category of formal elliptic spaces and, in general, whenever the total space
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Norm-attaining lattice homomorphisms Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-07-26 Sheldon Dantas, Gonzalo Martínez-Cervantes, José David Rodríguez Abellán, Abraham Rueda Zoca
In this paper we study the structure of the set ${\rm Hom}(X,\mathbb{R})$ of all lattice homomorphisms from a Banach lattice $X$ into $\mathbb{R}$. Using the relation among lattice homomorphisms and disjoint families, we prove that the topological dual of the free Banach lattice ${\rm FBL}(A)$ generated by a set $A$ contains a disjoint family of cardinality $2^{|A|}$, answering a question of B. de
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Localized regularity of planar maps of finite distortion Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-07-13 Olli Hirviniemi, István Prause, Eero Saksmann
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion. Analogues of such results were known earlier in the case of quasiconformal mappings. Moreover, we study regularity for maps whose distortion has better than exponential
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On smooth Fano fourfolds of Picard number two Rev. Mat. Iberoam. (IF 1.2) Pub Date : 2021-07-13 Jürgen Hausen, Antonio Laface, Christian Mauz
We classify the smooth Fano 4-folds of Picard number two that have a general hypersurface Cox ring.