Electronic Resource
Springer
Geometric and functional analysis
10 (2000), S. 1028-1052
ISSN:
1420-8970
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We develop several applications of the Brunn—Minkowski inequality in the Prékopa—Leindler form. In particular, we show that an argument of B. Maurey may be adapted to deduce from the Prékopa—Leindler theorem the Brascamp—Lieb inequality for strictly convex potentials. We deduce similarly the logarithmic Sobolev inequality for uniformly convex potentials for which we deal more generally with arbitrary norms and obtain some new results in this context. Applications to transportation cost and to concentration on uniformly convex bodies complete the exposition.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00001645
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