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arXiv · 1606.02129

Maximal surface area of a convex set in $\mathbb{R}^n$ with respect to exponential rotation invariant measures

Galyna Livshyts
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Abstract

Let $p$ be a positive number. Consider probability measure $\gamma_p$ with density $\varphi_p(y)=c_{n,p}e^{-\frac{|y|^p}{p}}$. We show that the maximal surface area of a convex body in $\mathbb{R}^n$ with respect to $\gamma_p$ is asymptotically equal to $C_p n^{\frac{3}{4}-\frac{1}{p}}$, where constant $C_p$ depends on $p$ only. This is a generalization of Ball's and Nazarov's bounds, which were given for the case of the standard Gaussian measure $\gamma_2$.

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Galyna Livshyts. 2016-06-07. Maximal surface area of a convex set in $\mathbb{R}^n$ with respect to exponential rotation invariant measures. https://arxiv.org/abs/1606.02129

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