Stability of the Cone-Volume Measure With Near Constant Density

Yingxiang Hu; Mohammad N. Ivaki

doi:10.1093/imrn/rnaf062

Stability of the Cone-Volume Measure With Near Constant Density

Yingxiang Hu
, Mohammad N. Ivaki^*

^*Corresponding author for this work

School of Mathematical Sciences

TU Wien

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Article number	rnaf062
Journal	International Mathematics Research Notices
Volume	2025
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnaf062
State	Published - 1 Mar 2025

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title = "Stability of the Cone-Volume Measure With Near Constant Density",

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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AB - 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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Stability of the Cone-Volume Measure With Near Constant Density

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