The globalization theorem for the curvature-dimension condition
From MaRDI portal
Publication:2238045
DOI10.1007/s00222-021-01040-6zbMath1479.53049arXiv1612.07623OpenAlexW3189569312MaRDI QIDQ2238045
Fabio Cavalletti, Emanuel Milman
Publication date: 29 October 2021
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.07623
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Spaces of measures, convergence of measures (28A33) Manifolds and measure-geometric topics (49Q99)
Related Items (72)
Boundary regularity and stability for spaces with Ricci bounded below ⋮ Isoperimetric sets in spaces with lower bounds on the Ricci curvature ⋮ A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on 𝑅𝐶𝐷(𝐾,𝑁) spaces ⋮ On quotients of spaces with Ricci curvature bounded below ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Ball covering property and number of ends of \(\mathsf{CD}\) spaces with non-negative curvature outside a compact set ⋮ An upper bound on the revised first Betti number and a torus stability result for \textsf{RCD} spaces ⋮ Quantitative maximal volume entropy rigidity on Alexandrov spaces ⋮ Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds ⋮ The isoperimetric problemviadirect method in noncompact metric measure spaces with lower Ricci bounds ⋮ Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces ⋮ Radial processes on \(\mathsf{RCD}^\ast(K,N)\) spaces ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ Quasiconformal mappings and curvatures on metric measure spaces ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ On master test plans for the space of BV functions ⋮ Moduli spaces of compact \(\mathrm{RCD}(0,N)\)-structures ⋮ First-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spaces ⋮ Differential Harnack inequalities for semilinear parabolic equations on \(\mathrm{RCD}^{\ast} (K,N)\) metric measure spaces ⋮ One dimensional 𝖱𝖢𝖣 spaces always satisfy the regular Weyl’s law ⋮ The dynamical Schrödinger problem in abstract metric spaces ⋮ Failure of strong unique continuation for harmonic functions on RCD spaces ⋮ A review of Lorentzian synthetic theory of timelike Ricci curvature bounds ⋮ The rigidity of sharp spectral gap in non-negatively curved spaces ⋮ Quantitative rigidity of almost maximal volume entropy for both \(\mathsf{RCD}^\ast\) spaces and integral Ricci curvature bound ⋮ Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds ⋮ Rényi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions ⋮ Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below ⋮ Unique continuation problem on RCD spaces. I ⋮ Subgraphs of BV functions on RCD spaces ⋮ Extremal of log-Sobolev functionals and Li-Yau estimate on \(\mathrm{RCD}^* (K,N)\) spaces ⋮ A synthetic null energy condition ⋮ The Brunn-Minkowski inequality implies the CD condition in weighted Riemannian manifolds ⋮ The metric measure boundary of spaces with Ricci curvature bounded below ⋮ An optimal transport formulation of the Einstein equations of general relativity ⋮ Equivalent definitions of very strict \textit{CD(K,N)}-spaces ⋮ Three-Dimensional Alexandrov Spaces: A Survey ⋮ Topological and Geometric Rigidity for Spaces with Curvature Bounded Below ⋮ Obstacle problems on \(\mathrm{RCD}(K, N)\) metric measure spaces ⋮ An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth ⋮ Good geodesics satisfying the timelike curvature-dimension condition ⋮ On the notion of Laplacian bounds on 𝑅𝐶𝐷 spaces and applications ⋮ Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications ⋮ Quantitative Obata's theorem ⋮ The globalization theorem for \(\mathrm{CD}(K, N)\) on locally finite spaces ⋮ The isoperimetric problem on Riemannian manifolds via Gromov–Hausdorff asymptotic analysis ⋮ The Cheeger problem in abstract measure spaces ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ The behavior of harmonic functions at singular points of \(\mathsf{RCD}\) spaces ⋮ Bakry-Émery conditions on almost smooth metric measure spaces ⋮ Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary ⋮ Collapsed Ricci limit spaces as non-collapsed RCD spaces ⋮ Polya-Szego inequality and Dirichlet \(p\)-spectral gap for non-smooth spaces with Ricci curvature bounded below ⋮ The equality case in Cheeger's and Buser's inequalities on \(\mathsf{RCD}\) spaces ⋮ Convergence to the product of the standard spheres and eigenvalues of the Laplacian ⋮ Localized elliptic gradient estimate for solutions of the heat equation on \({ RCD}^\ast(K,N)\) metric measure spaces ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ Isometric immersions of RCD spaces ⋮ Kantorovich problems and conditional measures depending on a parameter ⋮ A sufficient condition to a regular set being of positive measure on spaces ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Isoperimetric inequality under measure-contraction property ⋮ A Lorentzian analog for Hausdorff dimension and measure ⋮ Cheeger bounds on spin-two fields ⋮ Entropy-transport distances between unbalanced metric measure 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 ⋮ Curvature-dimension conditions under time change
Cites Work
- On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces
- Optimal maps and exponentiation on finite-dimensional spaces with Ricci curvature bounded from below
- Local curvature-dimension condition implies measure-contraction property
- 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
- 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
- Localization and tensorization properties of the curvature-dimension condition for metric measure spaces. II
- An optimal Poincaré inequality for convex domains
- Weak curvature conditions and functional inequalities
- Functions of bounded variation on ``good metric spaces
- Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
- Finsler interpolation inequalities
- Differentiability of Lipschitz functions on metric measure spaces
- Some applications of mass transport to Gaussian-type inequalities
- A convexity principle for interacting gases
- Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
- Fine properties of sets of finite perimeter in doubling metric measure spaces
- Needle decompositions and isoperimetric inequalities in Finsler geometry
- Isoperimetric problems for convex bodies and a localization lemma
- The Monge problem for distance cost in geodesic spaces
- Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
- 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
- Hamilton-Jacobi semigroup on length spaces and applications
- 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
- Monge problem in metric measure spaces with Riemannian curvature-dimension condition
- Decomposition of geodesics in the Wasserstein space and the globalization problem
- Metric measure spaces with Riemannian Ricci curvature bounded from below
- On the measure contraction property of metric measure spaces
- On local Poincaré via transportation
- On the geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Non-branching geodesics and optimal maps in strong \(CD(K,\infty)\)-spaces
- \((K,N)\)-convexity and the curvature-dimension condition for negative \(N\)
- Monge’s transport problem on a Riemannian manifold
- Failure of the local-to-global property for CD(K,N) spaces
- Alexandrov meets Lott--Villani--Sturm
- On the differential structure of metric measure spaces and applications
- Beyond traditional Curvature-Dimension I: New model spaces for isoperimetric and concentration inequalities in negative dimension
- Transport inequalities, gradient estimates, entropy and Ricci curvature
- Polar factorization and monotone rearrangement of vector‐valued functions
- Differential equations methods for the Monge-Kantorovich mass transfer problem
- Analysis and Geometry of Markov Diffusion Operators
- An overview of L1 Optimal Transportation on metric measure 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
- Five lectures on optimal transportation: Geometry, regularity and applications
- Optimal maps in essentially non-branching spaces
- Self-intersection of optimal geodesics
- The Exact Peano Derivative
- Optimal Transport
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: The globalization theorem for the curvature-dimension condition