M. Beltagy
Sufficient conditions for convexity in manifolds without focal points

Comment.Math.Univ.Carolinae 34,3 (1993) 443-449.

Abstract:In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings.

Keywords: supporting of subsets, convex subsets (hypersurfaces), conjugate (focal) points, horospheres
AMS Subject Classification: 53C42