Noncompact lp-minkowski problems
Publication Name
Indiana University Mathematics Journal
Abstract
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.
Open Access Status
This publication may be available as open access
Volume
70
Issue
3
First Page
855
Last Page
880
Funding Number
11926317
Funding Sponsor
Australian Research Council