Flag numbers and floating bodies

被引：4
作者：
Besau, Florian [1 ]
Schuett, Carsten [2 ]
Werner, Elisabeth M. [3 ,4 ]
机构：
[1] Goethe Univ Frankfurt, Inst Math, Robert Mayer Str 10, D-60054 Frankfurt, Germany
[2] Univ Kiel, Math Seminar, Kiel, Germany
[3] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA
[4] Univ Lille 1, UFR Math, F-59655 Villeneuve Dascq, France
来源：
ADVANCES IN MATHEMATICS | 2018年 / 338卷
关键词：
Convex floating body of polytope; Weighted floating body of polytope; Total number of flags; Flag simplex; Spherical polytope; Hyperbolic polytope; MINIMAL VOLUME PRODUCT; AFFINE SURFACE; CONVEX-BODIES; BLASCHKE-SANTALO; F-VECTORS; FACES; DIVERGENCE; STABILITY; POLYTOPES;
D O I：
10.1016/j.aim.2018.09.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate weighted floating bodies of polytopes. We show that the weighted volume depends on the complete flags of the polytope. This connection is obtained by introducing flag simplices, which translate between the metric and combinatorial structure. Our results are applied in spherical and hyperbolic space. This leads to new asymptotic results for polytopes in these spaces. We also provide explicit examples of spherical and hyperbolic convex bodies whose floating bodies behave completely different from any convex body in Euclidean space. (C) 2018 Elsevier Inc. All rights reserved.
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收藏
页码：912 / 952
页数：41
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