Title

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

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Link to publisher version (DOI)

http://dx.doi.org/10.1512/IUMJ.2021.70.8432