Rigidity of some functional inequalities on RCD spaces (Q2224711)

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scientific article

Language	Label	Description	Also known as
English	Rigidity of some functional inequalities on RCD spaces	scientific article

Statements

scholarly article

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Rigidity of some functional inequalities on RCD spaces (English)

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Journal de Mathématiques Pures et Appliquées. Neuvième Série

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publication date

4 February 2021

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full work available at URL

https://arxiv.org/abs/2001.07930

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zbMATH Keywords

Bakry-Émery inequality

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Ricci curvature

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metric measure space

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rigidity

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MaRDI profile type

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CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES

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Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces

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Equivalent definitions of \(BV\) space and of total variation on metric measure spaces

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Perimeter as relaxed Minkowski content in metric measure spaces

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Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure

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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

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Metric measure spaces with Riemannian Ricci curvature bounded from below

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Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds

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Gaussian-type isoperimetric inequalities in \(\mathsf{RCD}(K,\infty)\) probability spaces for positive \(K\)

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Well-posedness of Lagrangian flows and continuity equations in metric measure spaces

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Analysis and Geometry of Markov Diffusion Operators

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Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator

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An isoperimetric inequality on the discrete cube and an elementary proof of the isoperimetric inequality in Gauss space

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Phi-entropy inequalities for diffusion semigroups

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On the cases of equality in Bobkov's inequality and Gaussian rearrangement

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An overview of L1 Optimal Transportation on metric measure spaces

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Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities

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Differentiability of Lipschitz functions on metric measure spaces

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Eigenvalues of the drifted Laplacian on complete metric measure spaces

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An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature

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On the differential structure of metric measure spaces and applications

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Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below

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The continuity equation on metric measure spaces

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Independence on \(p\) of weak upper gradients on \(\mathsf{RCD}\) spaces

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From log Sobolev to Talagrand: A quick proof

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Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

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Characterizations of monotonicity of vector fields on metric measure spaces

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New characterizations of Ricci curvature on RCD metric measure spaces

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Ricci tensor on \(\mathrm{RCD}^\ast(K,N)\) spaces

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Book Review: Geometry of isotropic convex bodies

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Dimension-free Harnack inequalities on \(\mathrm{RCD}(K, \infty )\) spaces

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Hamilton-Jacobi semigroup on length spaces and applications

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Weak curvature conditions and functional inequalities

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Ricci curvature for metric-measure spaces via optimal transport

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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality

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Local Poincaré inequalities from stable curvature conditions on metric spaces

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Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces

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On the geometry of metric measure spaces. I

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Lipschitz algebras and derivations. II: Exterior differentiation

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Ricci curvature on Alexandrov spaces and rigidity theorems

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Identifiers

zbMATH Open document ID

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10.1016/j.matpur.2020.07.004

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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