Rigidity of Alexandrov Spaces

DOI10.1007/978-3-030-99298-9_1zbMath1529.53041OpenAlexW4312315315MaRDI QIDQ6165746

Peter V Petersen

Publication date: 2 August 2023

Published in: Recent Advances in Alexandrov Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-99298-9_1

zbMATH Keywords

rigidityAlexandrov geometryboundary convexity

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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• Deformations of the hemisphere that increase scalar curvature
• Three-dimensional Alexandrov spaces with positive or nonnegative Ricci curvature
• Scalar curvature rigidity of asymptotically hyperbolic spin manifolds
• A radius sphere theorem
• Parallel transportation for Alexandrov space with curvature bounded below
• Regularity of limits of noncollapsing sequences of manifolds
• Orientation and symmetries of Alexandrov spaces with applications in positive curvature
• Rigidity for positively curved Alexandrov spaces with boundary
• The boundary conjecture for leaf spaces
• Extrinsic curvature of semiconvex subspaces in Alexandrov geometry
• Rigidity theorems for compact manifolds with boundary and positive Ricci curvature
• A generalization of Berger's rigidity theorem for positively curved manifolds
• Globalization with probabilistic convexity
• On Three-Dimensional Alexandrov Spaces
• Semiconcave functions in Alexandrov's geometry
• Open map theorem for metric spaces
• A.D. Alexandrov spaces with curvature bounded below
• Index parity of closed geodesics and rigidity of Hopf fibrations

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