Minkowski problem for complete noncompact convex hypersurfaces

Kai-Seng Chou, Xu-Jia Wang

DOI: http://dx.doi.org/10.12775/TMNA.1995.037

Abstract


We present some sufficient conditions on the existence of a complete noncompact
convex hypersurface whose Gauss curvature is equal to a prescribed
function on the unit sphere. By the Legendre transform this problem is reduced
to the solvability of the Monge-Ampère equation subject to certain boundary
conditions.

Keywords


The Minkowski problem; the Monge-Ampère equation

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