Noncompact lp-minkowski problems
Indiana University Mathematics Journal
In this paper, we prove the existence of complete, noncompact convex hypersurfaces whose p-curvature function is prescribed on a domain in the unit sphere. This problem is related to the solvability of Monge-Ampère type equations subject to certain boundary conditions depending on the value of p. The special case of p = 1 was previously studied by Pogorelov  and Chou-Wang . Here, we give some sufficient conditions for the solvability for general p . 1.
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Australian Research Council