Valuations on Log-Concave Functions

被引：1
|
作者：
Mussnig, Fabian [1 ]
机构：
[1] Tech Univ Wien, Inst Diskrete Math & Geometrie, Wiedner Hauptstr 8-10-1046, A-1040 Vienna, Austria
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 06期
基金：
奥地利科学基金会;
关键词：
Valuation; Log-concave function; SL(n) covariance; Translation covariance; Moment vector; Difference body; TRANSLATION INVARIANT VALUATIONS; P-MINKOWSKI VALUATIONS; CONVEX-SETS;
D O I：
10.1007/s12220-020-00539-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions.
引用
收藏
页码：6427 / 6451
页数：25
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