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Title: Closeness to spheres of hypersurfaces with normal curvature bounded below

For a Riemannian manifold M{sup n+1} and a compact domain Ω⊂ M{sup n+1} bounded by a hypersurface ∂Ω with normal curvature bounded below, estimates are obtained in terms of the distance from O to ∂Ω for the angle between the geodesic line joining a fixed interior point O in Ω to a point on ∂Ω and the outward normal to the surface. Estimates for the width of a spherical shell containing such a hypersurface are also presented. Bibliography: 9 titles.
Authors:
 [1] ;  [2]
  1. Sumy State University, Sumy (Ukraine)
  2. V. N. Karazin Kharkiv National University, Faculty of Mathematics and Mechanics, Kharkiv (Ukraine)
Publication Date:
OSTI Identifier:
22365874
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; DISTANCE; GEODESICS; MATHEMATICAL MANIFOLDS; PARTIAL DIFFERENTIAL EQUATIONS; RIEMANN SPACE; SURFACES