Journal of Differential Geometry

Affine images of isotropic measures

Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang

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Abstract

Necessary and sufficient conditions are given in order for a Borel measure on the Euclidean sphere to have an affine image that is isotropic. A sharp reverse affine isoperimetric inequality for Borel measures on the sphere is presented. This leads to sharp reverse affine isoperimetric inequalities for convex bodies.

Article information

Source
J. Differential Geom. Volume 99, Number 3 (2015), 407-442.

Dates
First available in Project Euclid: 25 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1424880981

Digital Object Identifier
doi:10.4310/jdg/1424880981

Mathematical Reviews number (MathSciNet)
MR3316972

Zentralblatt MATH identifier
1325.28004

Citation

Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong. Affine images of isotropic measures. J. Differential Geom. 99 (2015), no. 3, 407--442. doi:10.4310/jdg/1424880981. https://projecteuclid.org/euclid.jdg/1424880981.


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