A finite diameter theorem on \(RCD(K,\infty)\) spaces for positive \(K\)

DOI10.1007/s00209-016-1626-9zbMath1346.53041OpenAlexW2255490205MaRDI QIDQ303794

Publication date: 22 August 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-016-1626-9

zbMATH Keywords

relative entropy Bakry-Émery condition geodesically \(K\)-convex heat distributions infinitesimal Hilbertianity

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (1)

Two compactness theorems on Finsler manifolds with positive weighted Ricci curvature

Cites Work

Unnamed Item
Unnamed Item
Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
Local curvature-dimension condition implies measure-contraction property
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
Duality on gradient estimates and Wasserstein controls
Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
Ricci curvature of Markov chains on metric spaces
Finsler interpolation inequalities
Dirichlet forms and analysis on Wiener space
Differentiability of Lipschitz functions on metric measure spaces
On the structure of spaces with Ricci curvature bounded below. I
On the structure of spaces with Ricci curvature bounded below. II
On the structure of spaces with Ricci curvature bounded below. III
Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter
Lower bounds on Ricci curvature and the almost rigidity of warped products
Non-contraction of heat flow on Minkowski spaces
Ricci curvature for metric-measure spaces via optimal transport
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Metric measure spaces with Riemannian Ricci curvature bounded from below
On the measure contraction property of metric measure spaces
Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces
On the geometry of metric measure spaces. I
On the geometry of metric measure spaces. II
Heat Kernel Estimates with Application to Compactness of Manifolds
Transport inequalities, gradient estimates, entropy and Ricci curvature
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below
Heat Flow on Alexandrov Spaces
Analysis and Geometry of Markov Diffusion Operators
Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure

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