The centered dual and the maximal injectivity radius of hyperbolic surfaces

DeBlois, Jason

doi:10.2140/gt.2015.19.953

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The centered dual and the maximal injectivity radius of hyperbolic surfaces

Jason DeBlois

Geometry & Topology 19 (2015) 953–1014

DOI: 10.2140/gt.2015.19.953

Abstract

We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each $g \geq 2$ , to identify a constant $r_{g - 1, 2}$ such that the set of closed genus- $g$ hyperbolic surfaces with maximal injectivity radius at least $r$ is compact if and only if $r > r_{g - 1, 2}$ . The main tool is a version of the centered dual complex that we introduced earlier, a coarsening of the Delaunay complex. In particular, we bound the area of a compact centered dual two-cell below given lower bounds on its side lengths.

Keywords

hyperbolic surface, injectivity radius, packing, Delaunay

Mathematical Subject Classification 2010

Primary: 52C15, 57M50

References

Publication

Received: 5 September 2013

Revised: 19 March 2014

Accepted: 15 June 2014

Published: 10 April 2015

Proposed: Danny Calegari

Seconded: Ian Agol, Dmitri Burago

Authors

Jason DeBlois
Department of Mathematics University of Pittsburgh 301 Thackeray Hall Pittsburgh, PA 15260 USA
http://www.pitt.edu/~jdeblois

Volume 19, issue 2 (2015)