Uniqueness of solutions to a class of isotropic curvature problems

Mohammad N. Ivaki, Emanuel Milman

Research output: Contribution to journalArticlepeer-review

Abstract

Employing a local version of the Brunn-Minkowski inequality, we give a new and simple proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are the only closed, self-similar solutions of the Gauss curvature flow. Extensions to various nonlinearities are obtained, assuming the centroid of the enclosed convex body is at the origin. By applying our method to the Alexandrov-Fenchel inequality, we also show that origin-centred balls are the only solutions to a large class of even Christoffel-Minkowski type problems.

Original languageEnglish
Article number109350
JournalAdvances in Mathematics
Volume435
DOIs
StatePublished - 15 Dec 2023

Keywords

  • Christoffel-Minkowski type problems
  • Lp Minkowski problem
  • Lp dual Minkowski problem
  • Uniqueness

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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