An affine isoperimetric inequality for log-concave functions
Abstract
The authors gave an affine isoperimetric inequality LYZ2010 that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simplex. In this paper, we give a functional isoperimetric inequality for log-concave functions that contains the affine isoperimetric inequality of Lutwak, Yang and Zhang in LYZ2010.
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