The logarithmic Minkowski problem

Böröczky, Károly; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong

doi:10.1090/S0894-0347-2012-00741-3

The logarithmic Minkowski problem
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by Károly J. Böröczky, Erwin Lutwak, Deane Yang and Gaoyong Zhang

J. Amer. Math. Soc. 26 (2013), 831-852

DOI: https://doi.org/10.1090/S0894-0347-2012-00741-3

Published electronically: June 5, 2012

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Abstract:

In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.

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