Noncompact lp-minkowski problems

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 [28] and Chou-Wang [10]. Here, we give some sufficient conditions for the solvability for general p . 1.