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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The centered dual and the maximal injectivity radius of hyperbolic surfaces

Jason DeBlois

Geometry & Topology 19 (2015) 953–1014
Abstract

We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g 2, to identify a constant rg1,2 such that the set of closed genus-g hyperbolic surfaces with maximal injectivity radius at least r is compact if and only if r > rg1,2. 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