Affine images of isotropic measures

Károly J. Böröczky Hungarian Academy of Sciences Erwin Lutwak New York University Deane Yang New York University Gaoyong Zhang New York University

Convex and Discrete Geometry mathscidoc:1702.40001

Journal of Differential Geometry, 99, (3), 407-442, 2015
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.
convex geometry, affine geometry, integral geometry
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  title={Affine images of isotropic measures},
  author={Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  booktitle={Journal of Differential Geometry},
Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Affine images of isotropic measures. 2015. Vol. 99. In Journal of Differential Geometry. pp.407-442.
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