On the geometry of subsets of positive reach

DOI10.1007/s00229-004-0491-8zbMath1076.53043OpenAlexW2018544797MaRDI QIDQ704818

Alexander Lytchak

Publication date: 19 January 2005

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-004-0491-8

zbMATH Keywords

Riemannian manifoldmetric spacepositive reachCAT-spaceupper curvature bound

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

Warped products admitting a curvature bound ⋮ The reach of subsets of manifolds ⋮ Some geometric inequalities related to Liouville equation ⋮ Some regularity of submetries ⋮ A note on subsets of positive reach ⋮ Remarks on manifolds with two-sided curvature bounds ⋮ Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above ⋮ Extrinsic curvature of semiconvex subspaces in Alexandrov geometry ⋮ Metric-minimizing surfaces revisited ⋮ Almost convex subsets ⋮ Curvature measures and soap bubbles beyond convexity ⋮ The structure of submetries ⋮ Rubber bands, pursuit games and shy couplings ⋮ Estimating the reach of a manifold via its convexity defect function

Cites Work

• \(\mathcal FK\)-convex functions on metric spaces
• Almost convex subsets
• Geometric Curvature Bounds in Riemannian Manifolds with Boundary
• Curvature Measures
• Metric minimizing surfaces
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