Stability of the cone-volume measure with near constant density
Differential Geometry
2025-06-30 v2 Analysis of PDEs
Metric Geometry
Abstract
We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy of the body is close to the unit ball in the -distance.
Keywords
Cite
@article{arxiv.2408.06172,
title = {Stability of the cone-volume measure with near constant density},
author = {Yingxiang Hu and Mohammad N. Ivaki},
journal= {arXiv preprint arXiv:2408.06172},
year = {2025}
}