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The Brunn–Minkowski Inequality for then-dimensional Logarithmic Capacity of Convex Bodies

✍ Scribed by Andrea Colesanti; Paola Cuoghi

Publisher: Springer Netherlands
Year: 2005
Tongue: English
Weight: 267 KB
Volume: 22
Category: Article
ISSN: 0926-2601
DOI: 10.1007/s11118-004-1326-7

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Suppose that 0 0 and 0 1 are convex, open subsets of R N . Denote their convex combination by The Brunn Minkowski inequality says that (vol 0 t ) 1ÂN (1&t) vol 0 1ÂN 0 +t vol 0 1ÂN 1 for 0 t 1. Moreover, if there is equality for some t other than an endpoint, then the domains 0 1 and 0 0 are transl