Valuations and surface area measures

被引：48

作者：

Haberl, Christoph ^{[1
]}

Parapatits, Lukas ^{[1
]}

机构：

[1] Salzburg Univ, A-5020 Salzburg, Austria

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2014年 / 687卷

基金：

奥地利科学基金会;

关键词：

MINKOWSKI-FIREY THEORY; INVARIANT VALUATIONS; AFFINE; BODIES;

D O I：

10.1515/crelle-2012-0044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider valuations defined on polytopes containing the origin which have measures on the sphere as values. We show that the classical surface area measure is essentially the only such valuation which is SL(n) contravariant of degree one. Moreover, for all real p, an L-p version of the above result is established for GL(n) contravariant valuations of degree p. This provides a characterization of the L-p surface area measures from the L-p Brunn-Minkowski theory.

引用

页码：225 / 245

页数：21

共 43 条

[1]

Aczel J., 1989, ENGLISH, V31, pxiii + 462

[2] Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture [J].