Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces

zbMath1260.53121arXiv0911.4020MaRDI QIDQ2901919

Jan Rataj, Luděk Zajíček

Publication date: 31 July 2012

Full work available at URL: https://arxiv.org/abs/0911.4020

zbMATH Keywords

Riemannian manifoldMinkowski spacecritical pointAlexandrov spacedistance functionpositive reachfinite dimensional Banach spacedistance sphereDC manifold

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Convexity of real functions of several variables, generalizations (26B25) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

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Normal cycles and curvature measures of sets with d.c. boundary ⋮ Fine properties of the curvature of arbitrary closed sets ⋮ Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature

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