Existence of non-symmetric solutions to the Gaussian Minkowski problem
Yibin Feng, Weiru Liu, Lei Xu
TL;DR
This paper proves the existence of non-symmetric solutions to the Gaussian Minkowski problem by analyzing a related Monge-Ampère equation on the sphere, extending previous work on symmetric solutions.
Contribution
It introduces the first proof of non-symmetric solutions to the Gaussian Minkowski problem through a novel analytical approach.
Findings
Established existence of non-symmetric solutions
Extended the class of solutions beyond symmetric cases
Utilized Monge-Ampère equation techniques on the sphere
Abstract
Existence of symmetric solutions to the Gaussian Minkowski problem was established by Huang, Xi and Zhao. In this paper, we show the existence of non-symmetric solutions to this problem by studying the related Monge-Amp\`{e}re type equation on the sphere.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research