The L-p dual Minkowski problem and related parabolic flows

摘要

This paper concerns the L-p dual Minkowski problem, which amounts to solving a class of Monge-Ampere type equations on the sphere. Our main purpose is to show the existence of solutions to the problem for all p > 0 via the study of related parabolic flows. We also discuss the problem when p < 0. The regularity and uniqueness of the solutions are also studied. (C) 2021 Elsevier Inc. All rights reserved.