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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Geometric inequalities for a class of exponential measures


Authors: Hermann Koenig and Nicole Tomczak-Jaegermann
Journal: Proc. Amer. Math. Soc. 133 (2005), 1213-1221
MSC (2000): Primary 46B20, 52A21
Published electronically: November 19, 2004
MathSciNet review: 2117224
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Abstract: Using $M$-ellipsoids we prove versions of the inverse Santaló inequality and the inverse Brunn-Minkowski inequality for a general class of measures replacing the usual volume on $\mathbb{R}^n$. This class contains in particular the Gaussian measure on $\mathbb{R}^n$.


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Additional Information

Hermann Koenig
Affiliation: Mathematisches Seminar, Universitaet Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany
Email: hkoenig@math.uni-kiel.de

Nicole Tomczak-Jaegermann
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: nicole@ellpspace.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07862-1
PII: S 0002-9939(04)07862-1
Keywords: Asymptotic geometric analysis, Santal\'{o} and Brunn-Minkowski inequalities, $M$-ellipsoids
Received by editor(s): December 21, 2003
Published electronically: November 19, 2004
Additional Notes: The second named author holds the Canada Research Chair in Geometric Analysis.
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.