The rigidity of sharp spectral gap in non-negatively curved spaces

DOI10.1016/j.na.2022.113202OpenAlexW3205812689MaRDI QIDQ2683028

Yu Kitabeppu, Christian Ketterer, Sajjad Lakzian

Publication date: 3 February 2023

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.05045

zbMATH Keywords

rigidityfirst eigenvalueRCD spaces

Mathematics Subject Classification ID

Rigidity results (53C24) Analysis on metric spaces (30L99) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

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• On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces
• Sharp spectral gaps on metric measure spaces
• Characterization of low dimensional \(RCD^\ast(K, N)\) spaces
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
• A PDE approach to nonlinear potential theory in metric measure spaces
• Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Sharp estimate on the first eigenvalue of the \(p\)-Laplacian
• Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
• Nonlinear potential theory on metric spaces
• Isospectral closed Riemannian manifolds which are not locally isometric
• An optimal Poincaré inequality for convex domains
• On the spectral gap for compact manifolds
• Obata's rigidity theorem for metric measure spaces
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
• A construction of non-flat, compact irreducible Riemannian manifolds which are isospectral but not isometric
• Differentiability of Lipschitz functions on metric measure spaces
• Application of coupling method to the first eigenvalue on manifold
• General formula for lower bound of the first eigenvalue on Riemannian manifolds
• On the structure of spaces with Ricci curvature bounded below. I
• Critical sets of solutions to elliptic equations.
• Some new results on eigenvectors via dimension, diameter, and Ricci curvature
• Elliptic partial differential equations of second order
• On the structure of spaces with Ricci curvature bounded below. III
• Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes
• Second order differentiation formula on \(\mathsf{RCD}(K,N)\) spaces
• Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces
• Polya-Szego inequality and Dirichlet \(p\)-spectral gap for non-smooth spaces with Ricci curvature bounded below
• A sharp lower bound for the first eigenvalue on Finsler manifolds with nonnegative weighted Ricci curvature
• Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces
• A Talenti-type comparison theorem for \(\mathrm{RCD}(K,N)\) spaces and applications
• Boundary regularity and stability for spaces with Ricci bounded below
• Sharp \(p\)-Poincaré inequalities under measure contraction property
• Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds
• The globalization theorem for the curvature-dimension condition
• Sharp isoperimetric inequalities and model spaces for the curvature-dimension-diameter condition
• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Monge problem in metric measure spaces with Riemannian curvature-dimension condition
• A sharp lower bound for the first eigenvalue on Finsler manifolds
• Decomposition of geodesics in the Wasserstein space and the globalization problem
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the sufficiency of \(c\)-cyclical monotonicity for optimality of transport plans
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Sharp estimates on the first eigenvalue of the \(p\)-Laplacian with negative Ricci lower bound
• Non-branching geodesics and optimal maps in strong \(CD(K,\infty)\)-spaces
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• New formulas for the Laplacian of distance functions and applications
• On the differential structure of metric measure spaces and applications
• An area formula in metric spaces
• Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Rigidity for the spectral gap on Rcd(K, ∞)-spaces
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
• Book Review: Geometry of isotropic convex bodies
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• A Note About the Strong Maximum Principle on RCD Spaces
• A Remark on Zhong-Yang's Eigenvalue Estimate
• A General Chain Rule for Derivatives and the Change of Variables Formula for the Lebesgue Integral
• Optimal Transport
• The geometry of Markov diffusion generators
• Polar factorization of maps on Riemannian manifolds
• Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries

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