Document Type

Article

Publication Date

10-2010

Keywords

Convex, body, Star body, Geometric tomography, Gauss measure, Brunn-Minkowski inequality, Ehrhard's inequality, Dual Brunn-Minkowski theory, Radial sum

Abstract

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed and proved to be true in some significant special cases Throughout the study attention is paid to precise equality conditions and conditions on the coefficients of dilatation. Interesting links are found to the S-inequality and the (B) conjecture. An example is given to show that convexity is needed in the (B) conjecture.

Publication Title

Transactions of the American Mathematical Society

Volume

362

Issue

10

First Page

5333

Last Page

5353

Required Publisher's Statement

First published in Transactions of the American Mathematical Society in Volume 362, Number 10, 2010, published by the American Mathematical Society

Subjects - Topical (LCSH)

Convex domains; Concave functions; Convex bodies; Geometric tomography; Borel sets; Variable stars

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Included in

Mathematics Commons

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