Quantitative maximal volume entropy rigidity on Alexandrov spaces

DOI10.1090/proc/15904zbMath1495.53062arXiv2007.14061OpenAlexW3046007317MaRDI QIDQ5081538

Lina Chen

Publication date: 15 June 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.14061

zbMATH Keywords

hyperbolic manifoldAlexandrov spaceGromov-Hausdorff distance

Mathematics Subject Classification ID

Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (1)

Quantitative rigidity of almost maximal volume entropy for both \(\mathsf{RCD}^\ast\) spaces and integral Ricci curvature bound

Cites Work

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• Optimal maps and exponentiation on finite-dimensional spaces with Ricci curvature bounded from below
• Local curvature-dimension condition implies measure-contraction property
• Well-posedness of Lagrangian flows and continuity equations in metric measure spaces
• An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
• An integral formula for the volume entropy with applications to rigidity
• Ricci curvature on Alexandrov spaces and rigidity theorems
• From volume cone to metric cone in the nonsmooth setting
• Rigidité topologique sous l'hypothèse \flqq entropie majorée\frqq\ et applications
• Topological entropy for geodesic flows
• The fundamental groups of almost nonnegatively curved manifolds
• Isometry groups of singular spaces
• The isometry group of an \(\mathsf{RCD}^*\) space is Lie
• On the isometry group of \(RCD^*(K,N)\)-spaces
• The globalization theorem for the curvature-dimension condition
• On the universal cover and the fundamental group of an \(\mathsf{RCD}^\ast(K,N)\)-space
• Quantitative volume space form rigidity under lower Ricci curvature bound. I
• Ricci curvature for metric-measure spaces via optimal transport
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the measure contraction property of metric measure spaces
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Maximal bottom of spectrum or volume entropy rigidity in Alexandrov geometry
• New formulas for the Laplacian of distance functions and applications
• Alexandrov meets Lott--Villani--Sturm
• On the differential structure of metric measure spaces and applications
• Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
• Non-collapsed spaces with Ricci curvature bounded from below
• Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces
• Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces
• CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES
• Optimal Transport

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