Convex hypersurfaces with prescribed Gauss-Kronecker curvature
نویسندگان
چکیده
منابع مشابه
Existence of Convex Hypersurfaces with Prescribed Gauss-kronecker Curvature
Let f(x) be a given positive function in Rn+1. In this paper we consider the existence of convex, closed hypersurfaces X so that its GaussKronecker curvature at x ∈ X is equal to f(x). This problem has variational structure and the existence of stable solutions has been discussed by Tso (J. Diff. Geom. 34 (1991), 389–410). Using the Mountain Pass Lemma and the Gauss curvature flow we prove the ...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1991
ISSN: 0022-040X
DOI: 10.4310/jdg/1214447213