A remark on the Alexandrov-Fenchel inequality

被引：13
|
作者：
Wang, Xu [1 ]
机构：
[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 274卷 / 07期
关键词：
Alexandrov-Fenchel inequality; Brascamp-Lieb proof; Khovanskii-Teissier inequality; T-Hodge theory; BRUNN-MINKOWSKI; EQUATION;
D O I：
10.1016/j.jfa.2018.01.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we give a complex-geometric proof of the Alexandrov-Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop the Brascamp-Lieb proof of the Prelcopa theorem. New ingredients in our proof include an integration of Timorin's mixed Hodge-Riemann bilinear relation and a mixed norm version of Harmander's L-2-estimate, which also implies a non-compact version of the Khovanskii-Teissier inequality. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：2061 / 2088
页数：28
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