Gaussian Brunn-Minkowski inequalities
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- by Richard J. Gardner and Artem Zvavitch PDF
- Trans. Amer. Math. Soc. 362 (2010), 5333-5353 Request permission
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.References
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Additional Information
- Richard J. Gardner
- Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225-9063
- MR Author ID: 195745
- Email: Richard.Gardner@wwu.edu
- Artem Zvavitch
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- MR Author ID: 671170
- Email: zvavitch@math.kent.edu
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5333-5353
- MSC (2010): Primary 52A20, 52A40, 60E15, 60G15
- DOI: https://doi.org/10.1090/S0002-9947-2010-04891-3
- MathSciNet review: 2657682