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arXiv · 2408.06172

Stability of the cone-volume measure with near constant density

Yingxiang Hu·Mohammad N. Ivaki
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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 $L^2$-distance.

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Yingxiang Hu, Mohammad N. Ivaki. 2024-08-12. Stability of the cone-volume measure with near constant density. https://doi.org/10.1093/imrn%2Frnaf062

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