Calculus of Variations and Geometric Measure Theory
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E. Carlen - F. Maggi

Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range non-local isoperimetry

created by maggi on 13 Jul 2015
modified on 06 Jun 2016


Accepted Paper

Inserted: 13 jul 2015
Last Updated: 6 jun 2016

Journal: Canadian J. Math.
Year: 2016


We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the Brunn-Minkowski inequality (for Minkowski sums between generic sets and convex sets) and of the Gaussian concentration inequality. The former inequality is then used to obtain a robust improvement of the Riesz rearrangement inequality under certain natural conditions. These conditions are compatible with the applications to a finite-range nonlocal isoperimetric problem arising in statistical mechanics.


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