On the planar Gaussian-Minkowski problem

Shibing Chen, Shengnan Hu, Weiru Liu, Yiming Zhao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered disk. As an application, this “uniqueness” result is used to prove the existence of smooth small solutions to the Gaussian-Minkowski problem via a degree-theoretic approach.

Original languageEnglish (US)
Article number109351
JournalAdvances in Mathematics
Volume435
DOIs
StatePublished - Dec 15 2023

Keywords

  • Degree theory
  • Gaussian Minkowski problem
  • Minkowski problems
  • Monge-Ampère equations

ASJC Scopus subject areas

  • General Mathematics

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