Bakry-Émery conditions on almost smooth metric measure spaces

DOI10.1515/agms-2018-0007zbMath1405.53055arXiv1804.07043OpenAlexW2963206386WikidataQ126000268 ScholiaQ126000268MaRDI QIDQ1712892

Shouhei Honda

Publication date: 1 February 2019

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.07043

zbMATH Keywords

Ricci curvaturemetric measure space

Mathematics Subject Classification ID

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 (4)

Heat kernel bounds and Ricci curvature for Lipschitz manifolds ⋮ Unique continuation problem on RCD spaces. I ⋮ New differential operator and noncollapsed RCD spaces ⋮ Sobolev-to-Lipschitz property on \({\mathsf{QCD}} \)-spaces and applications

Cites Work

• Unnamed Item
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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
• Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
• Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Ricci curvature and \(L^{p}\)-convergence
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Structure theory of singular spaces
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• Differentiability of Lipschitz functions on metric measure spaces
• On the structure of spaces with Ricci curvature bounded below. III
• Lower bounds on Ricci curvature and the almost rigidity of warped products
• Stratified spaces and synthetic Ricci curvature bounds
• The globalization theorem for the curvature-dimension condition
• Failure of topological rigidity results for the measure contraction property
• 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
• A weakly second-order differential structure on rectifiable metric measure spaces
• Cheeger-harmonic functions in metric measure spaces revisited
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Generalized doubling meets Poincaré
• On the geometry of metric measure spaces. I
• On the differential structure of metric measure spaces and applications
• Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
• SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES
• Sobolev met Poincaré
• Non-collapsed spaces with Ricci curvature bounded from below
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure

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