Volumes of Picard modular surfaces

Details Volumes of Picard modular surfaces Volumes of Picard modular surfaces

2010-05-24

arxiv.org/abs/1005.4436v2

Mathematics

Geometric Topology

To appear in Proceedings of the AMS

Scientific paper

We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal
volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. We then
show that every arithmetic cusped complex hyperbolic 2-manifold of minimal
volume covers one of these two orbifolds. We also give all minimal volume
manifolds that simultaneously cover both minimal orbifolds.

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