Metric-measure boundary and geodesic flow on Alexandrov spaces

DOI10.4171/JEMS/1006zbMath1493.53087arXiv1705.04767MaRDI QIDQ2659430

Vitali Kapovitch, Alexander Lytchak, Anton Petrunin

Publication date: 26 March 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.04767

zbMATH Keywords

geodesic flowLiouville measureconvex hypersurfacesAlexandrov spaces

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Momentum maps; symplectic reduction (53D20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Convex sets in (3) dimensions (including convex surfaces) (52A15) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Flows related to mean curvature (53E10)

Related Items (11)

Non-existence of concave functions on certain metric spaces ⋮ Boundary regularity and stability for spaces with Ricci bounded below ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ Asymptotically mean value harmonic functions in subriemannian and RCD settings ⋮ On continuous billiard and quasigeodesic flows characterizing alcoves and isosceles tetrahedra ⋮ The metric measure boundary of spaces with Ricci curvature bounded below ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces ⋮ Scalar curvature via local extent ⋮ On the topology and the boundary of \(N\)-dimensional \(\mathsf{RCD}\,(K,N)\) spaces ⋮ The structure of submetries

Cites Work

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• A.D. Alexandrov spaces with curvature bounded below
• Scalar curvature of definable CAT-spaces
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• Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

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