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ISSN 1088-6850(e) ISSN 0002-9947(p)

Gaussian Brunn-Minkowski inequalities

Author(s): Richard J. Gardner; Artem Zvavitch
Journal: Trans. Amer. Math. Soc. 362 (2010), 5333-5353.
MSC (2010): Primary 52A20, 52A40, 60E15, 60G15
Posted: May 20, 2010
MathSciNet review: 2657682
Retrieve article in: PDF

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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.

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