A new affine invariant for polytopes and Schneider's projection problem

被引：53

作者：

Lutwak, E ^{[1
]}

Yang, D ^{[1
]}

Zhang, GY ^{[1
]}

机构：

[1] Polytech Univ, Dept Math, Brooklyn, NY 11201 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 353卷 / 05期

关键词：

affine isoperimetric inequalities; reverse isoperimetric inequalities; projection bodies; asymptotic inequalities;

D O I：

10.1090/S0002-9947-01-02726-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New affine invariant functionals for convex polytopes are introduced. Some sharp affine isoperimetric inequalities are established for the new functionals. These new inequalities lead to fairly strong volume estimates for projection bodies. Two of the new affine isoperimetric inequalities are extensions of Ball's reverse isoperimetric inequalities.

引用

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页码：1767 / 1779

页数：13

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