Convexity of Hypersurfaces in Spherical Spaces

Details Convexity of Hypersurfaces in Spherical Spaces Convexity of Hypersurfaces in Spherical Spaces

2007-08-23

arxiv.org/abs/0708.3149v2

Mathematics

Metric Geometry

15 pages, 3 figures. Two more pictures. Corrections, mostly notational have been made. Proofs are given in more detail

Scientific paper

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.

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