Extrinsic curvature of semiconvex subspaces in Alexandrov geometry

DOI10.1007/s10455-009-9182-8zbMath1190.53073OpenAlexW2060092112WikidataQ125379188 ScholiaQ125379188MaRDI QIDQ2269469

Richard L. Bishop, Stephanie B. Alexander

Publication date: 16 March 2010

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-009-9182-8

zbMATH Keywords

rigiditygradient flowgeodesicinjectivity radiusAlexandrov spacecurvature boundsextrinsic curvaturehoroballLipschitz functionsemiconcave functionGauss equationstrong deformation retractionintrinsic curvature\(CAT(K)\) spaceangle/chord curvaturebase-angle/chord curvature.gradient curve

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Direct methods ((G)-spaces of Busemann, etc.) (53C70) Real-valued functions on manifolds (58C05)

Related Items (6)

Radius estimates for Alexandrov space with boundary ⋮ Comparison theorems for manifolds with mean convex boundary ⋮ On continuous billiard and quasigeodesic flows characterizing alcoves and isosceles tetrahedra ⋮ Rigidity of Alexandrov Spaces ⋮ Volume estimates for Alexandrov spaces with convex boundaries ⋮ Alexandrov spaces with maximal radius

Cites Work

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• Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above
• Almost convex subsets
• Semiconcave functions in Alexandrov's geometry
• An optimal extension of Perelman's comparison theorem for quadrangles and its applications
• Metric minimizing surfaces
• The curvature of minimal surfaces in singular spaces

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