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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Gaussian Brunn-Minkowski inequalities


Authors: Richard J. Gardner and Artem Zvavitch
Journal: Trans. Amer. Math. Soc. 362 (2010), 5333-5353
MSC (2010): Primary 52A20, 52A40, 60E15, 60G15
Published electronically: May 20, 2010
MathSciNet review: 2657682
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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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Additional Information

Richard J. Gardner
Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225-9063
Email: Richard.Gardner@wwu.edu

Artem Zvavitch
Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
Email: zvavitch@math.kent.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04891-3
PII: S 0002-9947(2010)04891-3
Keywords: Convex body, star body, geometric tomography, Gauss measure, Brunn-Minkowski inequality, Ehrhard's inequality, dual Brunn-Minkowski theory, radial sum
Received by editor(s): November 13, 2007
Received by editor(s) in revised form: July 3, 2008
Published electronically: May 20, 2010
Additional Notes: This work was supported in part by U.S. National Science Foundation grants DMS-0603307 and DMS-0504049.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.