Minkowski Problems for Complete Noncompact Convex Hypersurfaces
نویسندگان
چکیده
LetX be a compact, strictly convex C-hypersurface in the (n+1)-dimensional Euclidean space R. The Gauss map ofX maps the hypersurface one-to-one and onto the unit n-sphere S. One may parametrize X by the inverse of the Gauss map. Consequently, the Gauss curvature can be regarded as a function on S. The classical Minkowski problem asks conversely when a positive function K on S is the Gauss curvature of a compact convex hypersurface. It turns out that a necessary and sufficient condition is
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