Maximal surface area of a convex set in Rn with respect to exponential rotation invariant measures
نویسنده
چکیده
Let p be a positive number. Consider the probability measure γ p with density ϕ p (y) = c n,p e − |y| p p. We show that the maximal surface area of a convex body in R n with respect to γ p is asymptotically equivalent to C (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 γ 2 .
منابع مشابه
Maximal Surface Area of a Convex Set in R with Respect to Exponential Rotation Invariant
Let p be a positive number. Consider probability measure γp with density φp(y) = cn,pe − |y| p . We show that the maximal surface area of a convex body in R with respect to γp is asymptotically equal to Cpn 3 4 − 1 p , where constant Cp depends on p only. This is a generalization of Ball’s [Ba] and Nazarov’s [N] bounds, which were given for the case of the standard Gaussian measure γ2.
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