The logarithmic Minkowski problem for non-symmetric measures

Chen, Shibing; Li, Qi-rui; Zhu, Guangxian

doi:10.1090/tran/7499

The logarithmic Minkowski problem for non-symmetric measures
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by Shibing Chen, Qi-rui Li and Guangxian Zhu PDF

Trans. Amer. Math. Soc. 371 (2019), 2623-2641 Request permission

Abstract:

Recently, Böröczky, Lutwak, Yang, and Zhang [J. Amer. Math. Soc. 26 (2013), pp. 831–852] established necessary and sufficient conditions for the existence of solutions to the logarithmic Minkowski problem for origin-symmetric measures. We establish the existence of solutions to the logarithmic Minkowski problem for non-symmetric measures and demonstrate the non-uniqueness of solutions to the logarithmic Minkowski problem.

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