Bonn Topology Group - Abstracts

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Ruth Kellerhals (Fribourg): Hyperbolic orbifolds of minimal volume (14/01/2014)


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. We also present some new results about volume minimisers in dimensions six and eight related to Bugaenko's cocompact arithmetic Coxeter groups.

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