Hypersurfaces with free boundary in a convex conical domain in a space form

摘要

abstract_textpThis study presents rigidity results for hypersurfaces with free boundary in a convex conical domain in a space form. Let C be a conical domain with a piecewise linear boundary in a space form. A compact hypersurface with free boundary M subset of C is part of a geodesic sphere if either C is convex and M is an embedded and has constant higher order mean curvature, or H-1 does not vanish and the ratio H-r/H-t, l r, is constant on M./p/abstract_text