Noncompact $L_p$-Minkowski problems
Analysis of PDEs
2018-12-11 v1 Differential Geometry
Abstract
In this paper we prove the existence of complete, noncompact convex hypersurfaces whose -curvature function is prescribed on a domain in the unit sphere. This problem is related to the solvability of Monge-Amp\`ere type equations subject to certain boundary conditions depending on the value of . The special case of was previously studied by Pogorelov and Chou-Wang. Here, we give some sufficient conditions for the solvability for general .
Cite
@article{arxiv.1812.03309,
title = {Noncompact $L_p$-Minkowski problems},
author = {Yong Huang and Jiakun Liu},
journal= {arXiv preprint arXiv:1812.03309},
year = {2018}
}