THE LOGARITHMIC MINKOWSKI PROBLEM FOR NON-SYMMETRIC MEASURES

被引：79

作者：

Chen, Shibing ^{[1
]}

Li, Qi-Rui ^{[2
]}

Zhu, Guangxian ^{[3
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, 96 JinZhai Rd Baohe Dist, Hefei 230026, Anhui, Peoples R China

[2] Australian Natl Univ, Inst Math Sci, Canberra, ACT 2601, Australia

[3] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 371卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Cone-volume measure; logarithmic Minkowski problem; subspace concentration condition; SURFACE MEASURE; POLYTOPES; CLASSIFICATION; REGULARITY; UNIQUENESS; INVARIANT; GEOMETRY; SHAPES; SPHERE;

D O I：

10.1090/tran/7499

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently, Boroczky, 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.

引用

页码：2623 / 2641

页数：19

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