From volume cone to metric cone in the nonsmooth setting

DOI10.1007/s00039-016-0391-6zbMath1356.53049arXiv1512.03113OpenAlexW2963842420MaRDI QIDQ730024

Guido De Philippis, Nicola Gigli

Publication date: 23 December 2016

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03113

zbMATH Keywords

warped productmetric geometryrigidity theoremsoptimal transportvolume comparisoncurvature-dimension conditionsbounded Ricci curvatureRCD(0,N) condition

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)

Related Items (32)

Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces ⋮ Diffusion, optimal transport and Ricci curvature ⋮ Boundary regularity and stability for spaces with Ricci bounded below ⋮ Lecture notes on differential calculus on \(\mathsf{RCD}\) spaces ⋮ Non-compact \(\mathrm{RCD}(0,N)\) spaces with linear volume growth ⋮ On quotients of spaces with Ricci curvature bounded below ⋮ Non-collapsed spaces with Ricci curvature bounded from below ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Sobolev spaces on warped products ⋮ Quantitative maximal volume entropy rigidity on Alexandrov spaces ⋮ Cheeger-Colding-Tian theory for conic Kähler-Einstein metrics ⋮ On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds ⋮ Monotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spaces ⋮ Sobolev mappings between RCD spaces and applications to harmonic maps: a heat kernel approach ⋮ CD meets CAT ⋮ The metric measure boundary of spaces with Ricci curvature bounded below ⋮ Ricci curvature in dimension 2 ⋮ An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth ⋮ Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications ⋮ Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels ⋮ The behavior of harmonic functions at singular points of \(\mathsf{RCD}\) spaces ⋮ A Bishop-type inequality on metric measure spaces with Ricci curvature bounded below ⋮ Monotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spaces ⋮ Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary ⋮ Improved regularity estimates for Lagrangian flows on \(\mathrm{RCD}(K,N)\) spaces ⋮ Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces ⋮ Characterizations of monotonicity of vector fields on metric measure spaces ⋮ Stability of metric measure spaces with integral Ricci curvature bounds ⋮ Heat flow on time-dependent manifolds ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces ⋮ On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

Cites Work

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