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Some Functional Inequalities and Their Applications on Finsler Measure Spaces J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-15 Xinyue Cheng, Yalu Feng
We study functional and geometric inequalities on complete Finsler measure spaces with the weighted Ricci curvature \(\textrm{Ric}_\infty \) bounded below. We first obtain some local uniform Poincaré inequalities and Sobolev inequalities. Then, we prove a mean value inequality for nonnegative subsolutions of elliptic equations. Further, we derive local and global Harnack inequalities for positive harmonic
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Lipschitz-Volume Rigidity and Sobolev Coarea Inequality for Metric Surfaces J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-15 Damaris Meier, Dimitrios Ntalampekos
We prove that every 1-Lipschitz map from a closed metric surface onto a closed Riemannian surface that has the same area is an isometry. If we replace the target space with a non-smooth surface, then the statement is not true and we study the regularity properties of such a map under different geometric assumptions. Our proof relies on a coarea inequality for continuous Sobolev functions on metric
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Positive Intermediate Ricci Curvature with Maximal Symmetry Rank J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-15 Lee Kennard, Lawrence Mouillé
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Nonlinear Dirac Equation on Compact Spin Manifold with Chirality Boundary Condition J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-15 Yanyun Wen, Peihao Zhao
In this paper, we study the following nonlinear boundary value problem $$\begin{aligned} \left\{ \begin{array}{ll} D\psi -a(x)\psi =f(x,\psi )+\epsilon h(x,\psi )&{} \quad \hbox {on }M \\ B_{CHI}\psi =0 &{} \quad \hbox {on }\partial M \end{array} \right. \end{aligned}$$(D) where M is a compact Riemannian spin manifold of dimension\(m\ge 2\) and the boundary \(\partial M\) has non-negative mean curvature
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Small-Constant Uniform Rectifiability J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-14 Cole Jeznach
We provide several equivalent characterizations of locally flat, d-Ahlfors regular, uniformly rectifiable sets E in \({\mathbb {R}}^n\) with density close to 1 for any dimension \(d \in {\mathbb {N}}\), \(1 \le d < n\). In particular, we show that when E is Reifenberg flat with small constant and has Ahlfors regularity constant close to 1, then the Tolsa \(\alpha \) coefficients associated to E satisfy
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Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-12 Xing Fu, Jie Xiao, Qi Xiong
Abstract Getting inspired by the Caffarelli–Silvestre extensions, this paper investigates the weighted Lorentz–Sobolev capacities and their capacitary strong inequalities with applications to the Sobolev-type embeddings. Consequently, the weighted Lebesgue-Sobolev capacities and their applications to a functional inequality problem and the existence-regularity of solutions to the prototype p-Laplace
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Direct Minimization of the Canham–Helfrich Energy on Generalized Gauss Graphs J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-09 Anna Kubin, Luca Lussardi, Marco Morandotti
The existence of minimizers of the Canham–Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham–Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then lower semicontinuity and compactness are proved under a suitable condition on the bending constants ensuring coerciveness; the minimization follows by the
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Weighted K-Stability for a Class of Non-compact Toric Fibrations J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-09 Charles Cifarelli
We study the weighted constant scalar curvature, a modified scalar curvature introduced by Lahdili (Proc Lond Math Soc 119(4):1065–1114, 2019) depending on weight functions \((v, \, w)\), on non-compact semisimple principal toric fibrations. The latter notion is a generalization of the Calabi Ansatz originally defined by Apostolov et al. (J Differ Geom 68(2):277–345, 2004). This setup turns out to
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Lower Bounds for the First Eigenvalue of the p-Laplacian on Quaternionic Kähler Manifolds J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-09 Kui Wang, Shaoheng Zhang
We study the first nonzero eigenvalues for the p-Laplacian on quaternionic Kähler manifolds. Our first result is a lower bound for the first nonzero closed (Neumann) eigenvalue of the p-Laplacian on compact quaternionic Kähler manifolds. Our second result is a lower bound for the first Dirichlet eigenvalue of the p-Laplacian on compact quaternionic Kähler manifolds with smooth boundary. Our results
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The Heterotic-Ricci Flow and Its Three-Dimensional Solitons J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-09 Andrei Moroianu, Ángel J. Murcia, C. S. Shahbazi
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Ancient Solutions of Ricci Flow with Type I Curvature Growth J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-08 Stephen Lynch, Andoni Royo Abrego
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natural geometric assumptions. Nonnegatively curved solutions in dimensions 2 and 3, and uniformly PIC solutions in higher dimensions are now well understood. We consider ancient solutions of arbitrary dimension which are complete
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$$L^p_{loc}$$ Positivity Preservation and Liouville-Type Theorems J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-02 Andrea Bisterzo, Alberto Farina, Stefano Pigola
On a complete Riemannian manifold (M, g), we consider \(L^{p}_{loc}\) distributional solutions of the differential inequality \(-\Delta u + \lambda u \ge 0\) with \(\lambda >0\) a locally bounded function that may decay to 0 at infinity. Under suitable growth conditions on the \(L^{p}\) norm of u over geodesic balls, we obtain that any such solution must be nonnegative. This is a kind of generalized
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Pseudo-Kähler Geometry of Properly Convex Projective Structures on the torus J. Geom. Anal. (IF 1.1) Pub Date : 2024-03-01 Nicholas Rungi, Andrea Tamburelli
In this paper we prove the existence of a pseudo-Kähler structure on the deformation space \({\mathcal {B}}_0(T^2)\) of properly convex \({\mathbb {R}}{\mathbb {P}}^2\)-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of \({\mathcal {B}}_0(T^2)\) with the complement of the zero
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p-Carleson Measures in the Quaternionic Unit Ball with Applications to Slice Campanato and $$Q_p$$ Spaces J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-28 Cheng Yuan
The p-Carleson measure in the unit ball of quaternions is introduced in terms of the symmetric box. When \(p=1\) or \(p=2\), the p-Carleson measure becomes the Carleson measure for the Hardy or Bergman spaces, respectively. A criterion for a measure to be a p-Carleson measure is provided in terms of slice Cauchy kernels. Bergman type integral operators are shown to preserve the p-Carleson measure in
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Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-23 Juan Carlos Fernández, Oscar Palmas, Jonatán Torres Orozco
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Parabolicity of Invariant Surfaces J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-22
Abstract We present a clear and practical way to characterize the parabolicity of a complete immersed surface that is invariant with respect to a Killing vector field of the ambient space.
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Restricted Mean Value Property on Riemannian manifolds J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-22 Kingshook Biswas, Utsav Dewan
A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been studied mainly for domains in \(\mathbb {R}^n\), we consider this problem in the general setting of domains in Riemannian manifolds, and obtain results generalizing classical results of Fenton. We also obtain a result for complete, simply connected Riemannian
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Pluriclosed Flow and Hermitian-Symplectic Structures J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-22 Yanan Ye
We observe that pluriclosed flow preserves Hermitian-symplectic structures. And we extend pluriclosed flow to a flow of Hermitian-symplectic forms by adding an extra evolution equation, which is determined by the (2, 0)-part of Bismut–Ricci form. Moreover, we obtain a topological obstruction to the existence of global solutions in every dimension.
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Some Functional Properties on Cartan–Hadamard Manifolds of Very Negative Curvature J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-20 Ludovico Marini, Giona Veronelli
In this paper, we consider Cartan–Hadamard manifolds (i.e., simply connected, complete, of non-positive sectional curvature) whose negative Ricci curvature grows polynomially at infinity. We show that a number of functional properties, which typically hold on manifolds of bounded curvature, remain true in this setting. These include the characterization of Sobolev spaces on manifolds, the so-called
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Strict Monotonicity of the First q-Eigenvalue of the Fractional p-Laplace Operator Over Annuli J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-08 K. Ashok Kumar, Nirjan Biswas
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A Hessian-Dependent Functional With Free Boundaries and Applications to Mean-Field Games J. Geom. Anal. (IF 1.1) Pub Date : 2024-02-08 Julio C. Correa, Edgard A. Pimentel
We study a Hessian-dependent functional driven by a fully nonlinear operator. The associated Euler-Lagrange equation is a fully nonlinear mean-field game with free boundaries. Our findings include the existence of solutions to the mean-field game, together with Hölder continuity of the value function and improved integrability of the density. In addition, we prove the reduced free boundary is a set
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Dual Integrable Representations on Locally Compact Groups J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-30 Hrvoje Šikić, Ivana Slamić
Studies of various reproducing function systems emphasized the role of translations and the Fourier periodization function. These influenced the development of the concept of dual integrable representations, a large and important class of unitary representations on LCA groups. The key ingredient is the bracket function that enables the explicit description of corresponding cyclic spaces. Since its
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Classification of Solutions to Several Semi-linear Polyharmonic Equations and Fractional Equations J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-25 Zhuoran Du, Zhenping Feng, Yuan Li
We consider the following semi-linear equations $$\begin{aligned} (-\Delta )^pu=u^\gamma _+ ~~ \text{ in } {{\mathbb {R}}^n}, \end{aligned}$$ where \(\gamma \in (1,\frac{n+2p}{n-2p})\), \(n>2p>0\), \(u_+=\max \{u,0\}\), and \(2\le p\in {\mathbb {N}}\) or \(p\in (0,1)\). Subject to the integral constraint $$\begin{aligned} u_+^\gamma \in L^1({\mathbb {R}}^n), \end{aligned}$$ we obtain the classification
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A Sharp Sobolev Principle on the Graphic Submanifolds of $${\mathbb {R}}^{n+m}$$ J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-25 Jie Xiao, Fanheng Xu
This paper shows such a sharp Sobolev principle that if \((\Sigma ,g)\) is a compact n-dimensional graphic submanifold of \({\mathbb {R}}^{n+m}\), \(G=|\text {det}g|\) is the absolute value of the determinant of g, \(|B^n|\) is the volume of the open unit ball \(B^n\) in \({\mathbb {R}}^n\), and f is a positive smooth function on \(\Sigma \), then $$\begin{aligned} \left( \frac{\int _\Sigma |\nabla
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Legendrian Mean Curvature Flow in $$\eta $$ -Einstein Sasakian Manifolds J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-25 Shu-Cheng Chang, Yingbo Han, Chin-Tung Wu
Abstract Recently, there are a great deal of work done which connects the Legendrian isotopic problem with contact invariants. The isotopic problem of Legendre curve in a contact 3-manifold was studied via the Legendrian curve shortening flow which was introduced and studied by K. Smoczyk. On the other hand, in the SYZ Conjecture, one can model a special Lagrangian singularity locally as the special
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Existence and Concentration of Solutions to a Choquard Equation Involving Fractional p-Laplace via Penalization Method J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-25 Xin Zhang, Xueqi Sun, Sihua Liang, Van Thin Nguyen
In this paper, we study the Choquard equation involving \(\frac{N}{s}\)-fractional Laplace as follows: $$\begin{aligned} \varepsilon ^{ps}(-\Delta )_{p}^{s}u+V(x)|u|^{p-2}u= \varepsilon ^{\mu -N}\left[ \dfrac{1}{|x|^{\mu }}*F(u)\right] f(u)\;\text {in}\; \mathbb {R}^{N}, \end{aligned}$$ where \(\varepsilon \) is a positive parameter, \(N=ps, s\in (0,1), 0<\mu
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On Highly Degenerate CR Maps of Spheres J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Giuseppe della Sala, Bernhard Lamel, Michael Reiter, Duong Ngoc Son
For \(N \ge 4\) we classify the \((N-3)\)-degenerate smooth CR maps of the three-dimensional unit sphere into the \((2N-1)\)-dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain
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Global Solutions of 2-D Cubic Dirac Equation with Non-compactly Supported Data J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Qian Zhang
We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp time decay results for general cubic nonlinearities without additional structure. We also prove the scattering of the Dirac equation for certain classes of nonlinearities. In all the above results we do not require the initial data to have compact support.
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Gaps in the Support of Canonical Currents on Projective K3 Surfaces J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Simion Filip, Valentino Tosatti
We construct examples of canonical closed positive currents on projective K3 surfaces that are not fully supported on the complex points. The currents are the unique positive representatives in their cohomology classes and have vanishing self-intersection. The only previously known such examples were due to McMullen on nonprojective K3 surfaces and were constructed using positive entropy automorphisms
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Well-Posedness of the Kadomtsev–Petviashvili-II in the Negative Sobolev Space with Respect to y Direction J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Zhaohui Huo
In this paper, we first establish some new dyadic bilinear estimates of KP-II equation. Then following some ideas in [7], we consider the Cauchy problem of the 2-D KP-II equation in negative Sobolev space with respect to y direction $$\begin{aligned} \partial _t u + \partial _{xxx}u+\partial _{x}^{-1}(\partial _{yy} )u +\partial _x (u^2) =0, \ (x,y,t) \in {\mathbb {R}}^3. \end{aligned}$$ It follows
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Subsets of Positive and Finite $$\Psi _t$$ -Hausdorff Measures and Applications J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Bilel Selmi
Working with sets of infinite \(\Psi _t\)-Hausdorff measures can be cumbersome, so simplifying them to sets of positive finite general fractal measures proves to be highly beneficial. This paper aims to demonstrate that the \(\Psi _t\)-Hausdorff measures adhere to the property of being a subset of positive and finite measures. Our main result is then applied to establish that the general fractal function
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The Minimal Spherical Dispersion J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Joscha Prochno, Daniel Rudolf
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On Lipschitz Continuity and Smoothness Up to the Boundary of Solutions of Hyperbolic Poisson’s Equation J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Miodrag Mateljević, Nikola Mutavdžić
We solve the Dirichlet problem \(\left. u\right| _{{\mathbb {B}}^n}=\varphi ,\) for hyperbolic Poisson’s equation \(\Delta _h u=\mu \) where \(\varphi \in L^1(\partial {\mathbb {B}}^n)\) and \(\mu \) is a measure that satisfies a growth condition. Next we present a short proof for Lipschitz continuity of solutions of certain hyperbolic Poisson’s equations, previously established at Chen et al. (Calc
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On the Geometry of Steady Toric Kähler-Ricci Solitons J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Yury Ustinovskiy
In this paper we study gradient steady Kähler-Ricci soliton metrics on non-compact toric manifolds. We show that the orbit space of the free locus of such a manifold carries a natural Hessian structure with a nonnegative Bakry-Émery tensor. We generalize Calabi’s classical rigidity result and use this to prove that any complete \(\varvec{T}^n\)-invariant gradient steady Kähler-Ricci soliton with a
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Existence of an Effective Burning Velocity in a Cellular Flow for the Curvature G-Equation Proved Using a Game Analysis J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Hongwei Gao, Ziang Long, Jack Xin, Yifeng Yu
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The $$L_p$$ Chord Minkowski Problem for Negative p J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-19 Yuanyuan Li
Abstract In this paper, we solve the \(L_p\) chord Minkowski problem in the case of discrete measures whose supports are in general position for \(p<0\) and \(q>0.\) As for general Borel measure, we also give a proof but requiring \(-n< p<0\) and \(n+1>q\geqslant 1.\) The \(L_p\) chord Minkowski problem was recently posed by Lutwak, Xi, Yang, and Zhang, which seeks to determine the necessary and sufficient
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Boundedness of Operators on Weighted Morrey–Campanato Spaces in the Bessel Setting J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-13 Wenting Hu, Jorge J. Betancor, Shenyu Liu, Huoxiong Wu, Dongyong Yang
Let \(\lambda \in (-\frac{1}{2},\infty )\), and \(\{\mathcal {W}_{t}^{\lambda }\}_{t>0}\) be the heat semigroup related to the Bessel Schrödinger operator \(S_{\lambda }:=-\frac{d^2}{dx^2}+\frac{\lambda ^2-\lambda }{x^2}\) on \(\mathbb {R}_{+}:=(0, \infty )\). The authors introduce the weighted Morrey–Campanato space \(\mathrm{BMO^\alpha (\mathbb {R}_{+}, \omega )}\) with \(\alpha \in [0, 1)\) and
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Restriction Theorem for the Fourier–Dunkl Transform and Its Applications to Strichartz Inequalities J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-13 P. Jitendra Kumar Senapati, Pradeep Boggarapu, Shyam Swarup Mondal, Hatem Mejjaoli
Abstract In this article, we address the following Strichartz’s restriction problem: For a given surface S embedded in \(\mathbb {R}^{n}\times \mathbb {R}^{d}\) with \(n+d\ge 2\) , for what values of \(1\le p < 2,\) do we have $$\begin{aligned} \left( \int _S| {\widehat{f}}(\xi , \zeta ) |^2 h^2_\kappa (\zeta )d\sigma (\xi ,\zeta )\right) ^\frac{1}{2}\le C \Vert f\Vert _{L^p_\kappa (\mathbb R^n\times
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Ricci Flow Under Kato-Type Curvature Lower Bound J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-10 Man-Chun Lee
In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type curvature lower bound. As an application, we prove that any compact three-dimensional non-collapsed strong Kato limit space is homeomorphic to a smooth manifold. Moreover, similar result also holds in higher dimension under stronger curvature condition. We also use the Ricci
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Improved Caffarelli–Kohn–Nirenberg Inequalities and Uncertainty Principle J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-09 Pei Dang, Weixiong Mai
In this paper we prove some improved Caffarelli–Kohn–Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on \({\mathbb {R}}^n\), which is a further study of the results in Dang et al. (J Funct Anal 265:2239-2266, 2013). In particular, we introduce an analogue of “phase derivative" for vector-valued functions. Moreover, using the introduced “phase derivative", we
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The John–Nirenberg Space: Equality of the Vanishing Subspaces $$VJN_p$$ and $$CJN_p$$ J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-09 Riikka Korte, Timo Takala
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Boundary Recovery of Anisotropic Electromagnetic Parameters for the Time Harmonic Maxwell’s Equations J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-09 Sean Holman, Vasiliki Torega
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Facets of High-Dimensional Gaussian Polytopes J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-09 Károly J. Böröczky, Gábor Lugosi, Matthias Reitzner
We study the number of facets of the convex hull of n independent standard Gaussian points in \({\mathbb {R}}^d\). In particular, we are interested in the expected number of facets when the dimension is allowed to grow with the sample size. We establish an explicit asymptotic formula that is valid whenever \(d/n\rightarrow 0\). We also obtain the asymptotic value when d is close to n.
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Normalized Multi-peak Solutions to Nonlinear Elliptic Problems J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-09 Wenjing Chen, Xiaomeng Huang
In this article, we establish the existence of positive multi-peak solutions to the following elliptic problem $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta v+(\lambda +V(x))v=v^p \ {} &{}\text { in } \Omega ,\\ v>0 &{}\text { in }\Omega ,\\ \int _{\Omega }v^2dx=\rho , \end{array}\right. } \end{aligned}$$ where \(\Omega \) is a bounded smooth domain of \({\mathbb {R}}^N\) or the whole space
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Biharmonic Riemannian Submersions from a 3-Dimensional BCV Space J. Geom. Anal. (IF 1.1) Pub Date : 2024-01-05 Ze-Ping Wang, Ye-Lin Ou
BCV spaces are a family of 3-dimensional Riemannian manifolds which include six of Thurston’s eight geometries. In this paper, we give a complete classification of proper biharmonic Riemannian submersions from a 3-dimensional BCV space by proving that such biharmonic maps exist only in the cases of \(H^2\times \mathbb {R}\rightarrow \mathbb {R}^2\), or \({\widetilde{SL}}(2,\mathbb {R})\rightarrow \mathbb
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The First Width of Non-negatively Curved Surfaces with Convex Boundary J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-30 Sidney Donato, Rafael Montezuma
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Brunn–Minkowski Inequality for $$\theta $$ -Convolution Bodies via Ball’s Bodies J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 David Alonso-Gutiérrez, Javier Martín Goñi
Abstract We consider the problem of finding the best function \(\varphi _n:[0,1]\rightarrow {\mathbb {R}}\) such that for any pair of convex bodies \(K,L\in {\mathbb {R}}^n\) the following Brunn–Minkowski type inequality holds $$\begin{aligned} |K+_\theta L|^\frac{1}{n}\ge \varphi _n(\theta )(|K|^\frac{1}{n}+|L|^\frac{1}{n}), \end{aligned}$$ where \(K+_\theta L\) is the \(\theta \) -convolution body
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Normalized Solutions of Nonhomogeneous Mass Supercritical Schrödinger Equations in Bounded Domains J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Shijie Qi, Wenming Zou
This paper aims to consider normalized solutions of Schrödinger equations in bounded domains, that is, find \((\lambda ,u)\in \mathbb R\times H_0^1(\Omega )\) such that $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+\lambda u= |u|^{p-2}u+|u|^{q-2}u\quad &{}\text {in}\ \Omega ,\\ \int _{\Omega }u^2dx=\alpha , \end{array}\right. } \end{aligned}$$ where \(\Omega \subset \mathbb R^N\) is
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Quasilinear Schrödinger Equations With Stein-Weiss Type Convolution and Critical Exponential Nonlinearity in $${\mathbb {R}}^N$$ J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Reshmi Biswas, Sarika Goyal, K. Sreenadh
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Planar Pseudo-geodesics and Totally Umbilic Submanifolds J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Steen Markvorsen, Matteo Raffaelli
We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero mean curvature vector and such that the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. Such characterization is based
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Stable Geodesic Nets in Convex Hypersurfaces J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Herng Yi Cheng
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Some Inequalities for the Fourier Transform and Their Limiting Behaviour J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Nicola Garofalo
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Riemann–Hilbert Problems for Axially Symmetric Null-Solutions to Iterated Generalised Cauchy–Riemann Equations in $$\mathbb {R}^{n+1}$$ J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-29 Fuli He, Qian Huang, Min Ku
The Riemann–Hilbert boundary value problems with Clifford-algebra valued variable coefficients for null-solutions to iterated generalised Cauchy–Riemann equations, which are also so-called poly-monogenic functions, defined over axial symmetric domains of \(\mathbb {R}^{n+1}\), are studied in this context. The integral representation solutions to such problems and their solvable conditions are given
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Viscosity Solutions of Hamilton-Jacobi Equations in Proper $$\mathrm {CAT(0)}$$ Spaces J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-21 Othmane Jerhaoui, Hasnaa Zidani
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Existence and Stability of Normalized Solutions for Nonlocal Double Phase Problems J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-21 Mingqi Xiang, Yunfeng Ma
Abstract In this paper, we study the following nonlocal double phase problem involving the fractional p-Laplacian $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )_p^\alpha u+\mu \left[ u\right] ^{p-q}_{\beta ,q}(-\Delta )^{\beta }_q u =\lambda \left| u\right| ^{p-2}u+f(x,u)\ \ x\in \Omega ,\\ u=0\ \ \ x\in {\mathbb {R}}^N\setminus \Omega , \end{array}\right. }\end{aligned}$$ where \(0<\beta<\alpha<1
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A Generalization of the Schwarz Lemma for Transversally Harmonic Maps J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-21 Xin Huang, Weike Yu
In this paper, we consider transversally harmonic maps between Riemannian manifolds with Riemannian foliations. In terms of the Bochner techniques and sub-Laplacian comparison theorem, we are able to establish a generalization of the Schwarz lemma for transversally harmonic maps of bounded generalized transversal dilatation. In addition, we also obtain a Schwarz type lemma for transversally holomorphic
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Growth of Subsolutions of $$\Delta _p u = V|u|^{p-2}u$$ and of a General Class of Quasilinear Equations J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-16 Luis J. Alías, Giulio Colombo, Marco Rigoli
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Extremal Sections for a Trudinger–Moser Functional on Vector Bundle over a Closed Riemann Surface J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-16 Jie Yang, Yunyan Yang
Trudinger–Moser inequalities are important tools in partial differential equations and geometric analysis. Although there have been many results in this regard, there are few studies on vector valued function spaces. Years ago, joined with Y. Li and P. Liu, the second named author established a Trudinger–Moser inequality on vector bundle over a closed Riemann surface. In that article (Calc Var 28:59–87
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New Existence Results of the Planar $$L_p$$ Dual Minkowski Problem J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-16 Zhibo Cheng, Pedro J. Torres
We provide new sufficient conditions for the existence of a periodic solution of the second-order differential equation $$\begin{aligned} u''+u=u^{p-1}(u^2+u'^2)^{\frac{2-q}{2}}f(t), \end{aligned}$$ which is associated to the planar \(L_p\) dual Minkowski problem in convex geometry. The obtained conditions are complementary to recent results. The main tools in the proofs are a global continuation theorem
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The Shifted Wave Equation on Non-flat Harmonic Manifolds J. Geom. Anal. (IF 1.1) Pub Date : 2023-12-07 Oliver Brammen