Maximal surface area of a convex set in Rn with respect to exponential rotation invariant measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:404

Article

Livshyts, Galyna

关键词: Convex bodies;    Convex polytopes;    Surface area;    Gaussian measures;   

DOI  :  10.1016/j.jmaa.2013.03.014

来源: Elsevier

【 摘 要 】

Let p be a positive number. Consider the probability measure gamma(p) with density phi(p)(y) = c(n,p)e-(vertical bar y vertical bar p/p) . We show that the maximal surface area of a convex body in R-n with respect to gamma(p) is asymptotically equivalent to Cp(p)n(3/4-1/p), where the constant C(p) depends on p only. This is a generalization of results due to Ball (1993) [1] and Nazarov (2003) [9] in the case of the standard Gaussian measure gamma(2). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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