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.
Transactions of the American Mathematical Society
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First published in Transactions of the American Mathematical Society in Volume 362, Number 10, 2010, published by the American Mathematical Society
Gardner, Richard J. and Zvavitch, Artem, "Gaussian Brunn-Minkowski Inequalities" (2010). Mathematics. Paper 25.