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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
DOI: https://doi.org/10.1090/S0002-9939-04-07862-1
Published electronically: November 19, 2004
MathSciNet review: 2117224
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Abstract | References | Similar Articles | Additional Information

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 $\mathbb{R}^n$.


References [Enhancements On Off] (What's this?)

  • [BM] J. BOURGAIN AND V. D. MILMAN, New volume ratio properties for symmetric bodies in $\mathbb{R}^n$. Invent. Math. 88 (1987), no 2, 319-340. MR 0880954 (88f:52013)
  • [C] D. CORDERO-ERAUSQUIN, Santaló's inequality on $\mathbb{C}^n$ by complex interpolation. C. R. Acad. Sci. Paris Sér. I Math. 334 (2002), 767-772. MR 1905037 (2003f:32042)
  • [CFM] D. CORDERO-ERAUSQUIN, M. FRADELIZI AND B. MAUREY, The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems. preprint.
  • [G] R. J. GARDNER, The Brunn-Minkowski inequality. Bull. Amer. Math. Soc. 39 (2002), 355-405. MR 1898210 (2003f:26035)
  • [H] G. HARG´E, Une inégalité de décorrélation pour la measure Gaussienne. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 1325-1328. MR 1649146 (99h:60081)
  • [M] V. D. MILMAN, An inverse form of the Brunn-Minkowski inequality, with applications to the local theory of normed spaces. C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), 25-28. MR 0827101 (87f:52018)
  • [P] G. PISIER, Volumes of Convex Bodies and Banach Space Geometry. Cambridge Univ. Press, 1989. MR 1036275 (91d:52005)
  • [SSZ] G. SCHECHTMAN, TH. SCHLUMPRECHT AND J. ZINN, On the Gaussian measure of the intersection. Ann. Probab. 26 (1998), 346-357.MR 1617052 (99c:60032)

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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: https://doi.org/10.1090/S0002-9939-04-07862-1
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.

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