On the measure contraction property of metric measure spaces
From MaRDI portal
Publication:2468435
DOI10.4171/CMH/110zbMath1176.28016OpenAlexW2045049746MaRDI QIDQ2468435
Publication date: 23 January 2008
Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4171/cmh/110
Riemannian manifoldmeasure contraction propertyWasserstein spaceBonnet--Myers theoremGromov--Hausdorff convergence
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)
Related Items (only showing first 100 items - show all)
Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces ⋮ Tangent lines and Lipschitz differentiability spaces ⋮ Ricci curvature, isoperimetry and a non-additive entropy ⋮ Measure contraction properties of Carnot groups ⋮ A finite diameter theorem on \(RCD(K,\infty)\) spaces for positive \(K\) ⋮ \((K,N)\)-convexity and the curvature-dimension condition for negative \(N\) ⋮ Characterization of low dimensional \(RCD^\ast(K, N)\) spaces ⋮ Ricci curvature bounds for warped products ⋮ Sphere theorems with and without smoothing ⋮ On the structure of RCD spaces with upper curvature bounds ⋮ Non-compact \(\mathrm{RCD}(0,N)\) spaces with linear volume growth ⋮ Needle decompositions and isoperimetric inequalities in Finsler geometry ⋮ Synthetic theory of Ricci curvature bounds ⋮ Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigidities ⋮ Mini-workshop: Manifolds with lower curvature bounds. Abstracts from the mini-workshop held January 1--7, 2012 ⋮ Non-collapsed spaces with Ricci curvature bounded from below ⋮ Optimal maps and exponentiation on finite-dimensional spaces with Ricci curvature bounded from below ⋮ Optimal transport maps on Alexandrov spaces revisited ⋮ New formulas for the Laplacian of distance functions and applications ⋮ Quantitative maximal volume entropy rigidity on Alexandrov spaces ⋮ A first-order condition for the independence on \(p\) of weak gradients ⋮ On the geometry of metric measure spaces with variable curvature bounds ⋮ Transport maps, non-branching sets of geodesics and measure rigidity ⋮ Obata's rigidity theorem for metric measure spaces ⋮ Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces ⋮ Radial processes on \(\mathsf{RCD}^\ast(K,N)\) spaces ⋮ Ricci Bounds for Euclidean and Spherical Cones ⋮ Sharp \(p\)-Poincaré inequalities under measure contraction property ⋮ Existence and uniqueness of optimal transport maps ⋮ A review of Lorentzian synthetic theory of timelike Ricci curvature bounds ⋮ Nonlinear geometric analysis on Finsler manifolds ⋮ Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems ⋮ An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth ⋮ Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces ⋮ The Monge problem for distance cost in geodesic spaces ⋮ Local Poincaré inequalities from stable curvature conditions on metric spaces ⋮ Local curvature-dimension condition implies measure-contraction property ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels ⋮ The Geometric Meaning of Curvature: Local and Nonlocal Aspects of Ricci Curvature ⋮ Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ A topological splitting theorem for sub-Riemannian manifolds ⋮ A weakly second-order differential structure on rectifiable metric measure spaces ⋮ Contraction of measures on graphs ⋮ Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds ⋮ Parabolic Harnack inequality on metric spaces with a generalized volume property ⋮ Exact and asymptotic results on coarse Ricci curvature of graphs ⋮ Sectional curvature-type conditions on metric spaces ⋮ Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary ⋮ A Bonnet-Myers type theorem for quaternionic contact structures ⋮ On the spaces with Ricci curvature bounds ⋮ On the curvature and heat flow on Hamiltonian systems ⋮ Absolute continuity of Wasserstein geodesics in the Heisenberg group ⋮ Extremals of log Sobolev inequality on non-compact manifolds and Ricci soliton structures ⋮ Riemannian polyhedra and Liouville-type theorems for harmonic maps ⋮ Characterizing spaces satisfying Poincaré inequalities and applications to differentiability ⋮ On one-dimensionality of metric measure spaces ⋮ Sub-Riemannian interpolation inequalities ⋮ Ricci curvature of metric spaces ⋮ The globalization theorem for the curvature-dimension condition ⋮ On weak super Ricci flow through neckpinch ⋮ Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds ⋮ Sphere theorems for RCD and stratified spaces ⋮ Sharp Poincaré inequalities under Measure Contraction Property ⋮ Lower bound of coarse Ricci curvature on metric measure spaces and eigenvalues of Laplacian ⋮ Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs ⋮ A probabilistic approach to the maximal diameter theorem ⋮ Alexandrov spaces with large volume growth ⋮ On local Poincaré via transportation ⋮ Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations ⋮ A topological splitting theorem for weighted Alexandrov spaces ⋮ Bishop-Gromov type inequality on Ricci limit spaces ⋮ Localization and tensorization properties of the curvature-dimension condition for metric measure spaces ⋮ Curvature-dimension condition meets Gromov's \(n\)-volumic scalar curvature ⋮ On the topology and the boundary of \(N\)-dimensional \(\mathsf{RCD}\,(K,N)\) spaces ⋮ Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups ⋮ Sharp measure contraction property for generalized H-type Carnot groups ⋮ Left-invariant geometries on \(\operatorname{SU}(2)\) are uniformly doubling ⋮ Ricci curvature of Markov chains on metric spaces ⋮ Inner-outer curvatures, Ollivier-Ricci curvature and volume growth of graphs ⋮ Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds. ⋮ Stability of metric measure spaces with integral Ricci curvature bounds ⋮ A note on local gradient estimate on Alexandrov spaces ⋮ Displacement convexity of entropy and the distance cost optimal transportation ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ Ricci curvature of graphs ⋮ A discrete version of the Brunn-Minkowski inequality and its stability ⋮ Finsler interpolation inequalities ⋮ Weighted Littlewood-Paley inequalities for heat flows in RCD spaces ⋮ An integral type characterization of Lipschitz functions over metric-measure spaces ⋮ Distortion coefficients of the \(\alpha\)-Grushin plane ⋮ Isoperimetric inequality under measure-contraction property ⋮ Sobolev-to-Lipschitz property on \({\mathsf{QCD}} \)-spaces and applications ⋮ Independence of synthetic curvature dimension conditions on transport distance exponent ⋮ Cones over metric measure spaces and the maximal diameter theorem ⋮ Failure of topological rigidity results for the measure contraction property ⋮ How to lift positive Ricci curvature ⋮ Unnamed Item ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups
This page was built for publication: On the measure contraction property of metric measure spaces
