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Geometric inequalities for a class of exponential measures
Author(s):
Hermann
Koenig;
Nicole
Tomczak-Jaegermann
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1213-1221.
MSC (2000):
Primary 46B20, 52A21
Posted:
November 19, 2004
MathSciNet review:
2117224
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Abstract:
Using  -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  . This class contains in particular the Gaussian measure on  .
References:
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- [BM]
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 . Invent. Math. 88 (1987), no 2, 319-340. MR 0880954 (88f:52013) - [C]
- D. CORDERO-ERAUSQUIN, Santaló's inequality on
 by complex interpolation. C. R. Acad. Sci. Paris Sér. I Math. 334 (2002), 767-772. MR 1905037 (2003f:32042) - [CFM]
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- R. J. GARDNER, The Brunn-Minkowski inequality. Bull. Amer. Math. Soc. 39 (2002), 355-405. MR 1898210 (2003f:26035)
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- 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)
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- 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)
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- G. PISIER, Volumes of Convex Bodies and Banach Space Geometry. Cambridge Univ. Press, 1989. MR 1036275 (91d:52005)
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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:
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
Posted:
November 19, 2004
Additional Notes:
The second named author holds the Canada Research Chair in Geometric Analysis.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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