Journal of Differential Geometry

Affine images of isotropic measures

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

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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.

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

First available in Project Euclid: 25 February 2015

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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.

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