Hyperbolic orbifolds of minimal volume
| Autor: | Ruth Kellerhals |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Coxeter group Hyperbolic manifold 0102 computer and information sciences Point group 01 natural sciences Relatively hyperbolic group Algebra Mathematics::Group Theory Computational Theory and Mathematics 010201 computation theory & mathematics Coxeter complex Artin group Mathematics::Metric Geometry 0101 mathematics Longest element of a Coxeter group Coxeter element Analysis Mathematics |
| Zdroj: | Computational Methods and Function Theory Computational Methods and Function Theory |
| Popis: | We provide a survey of hyperbolic orbifolds of minimal volume, starting with the results of Siegel in two dimensions and with the contributions of Gehring, Martin and others in three dimensions. For higher dimensions, we summarise some of the most important results, due to Belolipetsky, Emery and Hild, by discussing related features such as hyperbolic Coxeter groups, arithmeticity and consequences of Prasad’s volume, as well as canonical cusps, crystallography and packing densities. We also present some new results about volume minimisers in dimensions six and eight related to Bugaenko’s cocompact arithmetic Coxeter groups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|