关于指数旋转不变测度的$\mathbb{R}^n$中凸集的最大表面积
Maximal surface area of a convex set in $\mathbb{R}^n$ with respect to exponential rotation invariant measures
摘要：
设$p$为正数。考虑概率测度$γ_p$和密度$φ_p(y)=c_{n,p}e^{-\frac{|y|^p}{p}}$。我们证明了$\mathbb{R}^n$中凸体关于$γ_p$的最大表面积渐近等于$C_p n^{\frac{3}{4}-\frac{1}{p}}$，其中常数$C_p$仅依赖于$p$.这是一个推广的球和纳扎罗夫的界限，这是给的情况下，标准高斯测度$γ_2$。
英文摘要：
Let $p$ be a positive number. Consider probability measure $γ_p$ with density $φ_p(y)=c_{n,p}e^{-\frac{|y|^p}{p}}$. We show that the maximal surface area of a convex body in $\mathbb{R}^n$ with respect to $γ_p$ 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 $γ_2$.
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