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

Let pp be a positive number. Consider the probability measure γpγp with density φp(y)=cn,pe−|y|pp. We show that the maximal surface area of a convex body in RnRn with respect to γpγp is asymptotically equivalent to C(p)n34−1p, where the constant C(p)C(p) depends on pp only. This is a generalization of results due to Ball (1993) [1] and Nazarov (2003) [9] in the case of the standard Gaussian measure γ2γ2.