Convexity of Hypersurfaces in Spherical Spaces
Metric Geometry
2007-10-02 v2 Differential Geometry
Abstract
A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold into the n-sphere is a surjection onto the boundary of a convex set.
Cite
@article{arxiv.0708.3149,
title = {Convexity of Hypersurfaces in Spherical Spaces},
author = {Konstantin Rybnikov},
journal= {arXiv preprint arXiv:0708.3149},
year = {2007}
}
Comments
15 pages, 3 figures. Two more pictures. Corrections, mostly notational have been made. Proofs are given in more detail