Stability of the cone-volume measure with near constant density

2024/08/12 by Hu, Yingxiang, Ivaki, Mohammad N. · 4 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2408.06172

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 L²-distance.

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