We are interested in Gaussian versions of the classical Brunn–Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp–Lieb inequality and of its reverse form, which follow exactly the same lines.
@article{10_4064_sm191_3_9,
author = {Franck Barthe and Nolwen Huet},
title = {On {Gaussian} {Brunn{\textendash}Minkowski} inequalities},
journal = {Studia Mathematica},
pages = {283--304},
year = {2009},
volume = {191},
number = {3},
doi = {10.4064/sm191-3-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm191-3-9/}
}
TY - JOUR
AU - Franck Barthe
AU - Nolwen Huet
TI - On Gaussian Brunn–Minkowski inequalities
JO - Studia Mathematica
PY - 2009
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EP - 304
VL - 191
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UR - http://geodesic.mathdoc.fr/articles/10.4064/sm191-3-9/
DO - 10.4064/sm191-3-9
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%J Studia Mathematica
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%N 3
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Franck Barthe; Nolwen Huet. On Gaussian Brunn–Minkowski inequalities. Studia Mathematica, Tome 191 (2009) no. 3, pp. 283-304. doi: 10.4064/sm191-3-9
