带奇点的常 Gauss 曲率曲面

Abstract

In this paper, we prove that a closed convex hypersurface of constant Gaussian curvature cannot possess only one singular point. If it has two singular points, it must be rotationally symmetric. We also show that for any convex polyhedron, there exist closed convex hypersurfaces of constant Gaussian curvature K0 such that the vertices of the polyhedron are the singular points of the hypersurface when K0 is sufficiently small. Show more