180 research outputs found
Hurwitz ball quotients
We consider the analogue of Hurwitz curves, smooth projective curves of
genus that realize equality in the Hurwitz bound , to smooth compact quotients of the unit ball in
. When is arithmetic, we show that , where is the (topological) Euler characteristic, and in the case
of equality show that is a regular cover of a particular Deligne--Mostow
orbifold. We conjecture that this inequality holds independent of
arithmeticity, and note that work of Xiao makes progress on this conjecture and
implies the best-known lower bound for the volume of a complex hyperbolic
-orbifold.Comment: Several improvements incorporating referee's comments. To appear in
Math.
A Cantor set with hyperbolic complement
We construct a Cantor set in S^3 whose complement admits a complete
hyperbolic metric
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