Monotonicity and concavity of integral functionals involving area measures of convex bodies

被引：5

作者：

Colesanti, Andrea ^{[1
]}

Hug, Daniel ^{[2
]}

Gomez, Eugenia Saorin ^{[3
]}

机构：

[1] Dipartimento Matemat & Informat Ulisse Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Karlsruhe Inst Technol, Dept Math, D-76128 Karlsruhe, Germany

[3] Otto von Guericke Univ, Fak Math, Univ Pl 2, D-39106 Magdeburg, Germany

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2017年 / 19卷 / 02期

关键词：

Convex bodies; Brunn-Minkowski inequality; area measure; monotonic functional; BRUNN-MINKOWSKI INEQUALITIES;

D O I：

10.1142/S0219199716500334

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a broad class of integral functionals defined on the space of n-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type inequality. In particular, we prove that a Brunn-Minkowski type inequality implies monotonicity, and that a general Brunn-Minkowski type inequality is equivalent to the functional being a mixed volume.

引用

页数：26

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