Flag numbers and floating bodies
| Autor: | Florian Besau, Elisabeth M. Werner, Carsten Schütt |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Euclidean space General Mathematics Hyperbolic space 010102 general mathematics Regular polygon Polytope 0102 computer and information sciences 01 natural sciences Connection (mathematics) 010201 computation theory & mathematics Metric (mathematics) Mathematics::Metric Geometry Convex body 0101 mathematics Mathematics Flag (geometry) |
| Zdroj: | Advances in Mathematics. 338:912-952 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2018.09.006 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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