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The Moduli Space of Riemann Surfaces of Large Genus

Fletcher, Alastair and Kahn, Jeremy and Markovic, Vladimir (2013) The Moduli Space of Riemann Surfaces of Large Genus. Geometric and Functional Analysis, 23 (3). pp. 867-887. ISSN 1016-443X. https://resolver.caltech.edu/CaltechAUTHORS:20130730-113506238

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Abstract

Let M_(g,ϵ) be the ϵ -thick part of the moduli space M_g of closed genus g surfaces. In this article, we show that the number of balls of radius r needed to cover M_(g,ϵ) is bounded below by (c_1g)^(2g) and bounded above by (c_2g)^(2g), where the constants c_1, c_2 depend only on ϵ and r, and in particular not on g. Using this counting result we prove that there are Riemann surfaces of arbitrarily large injectivity radius that are not close (in the Teichmüller metric) to a finite cover of a fixed closed Riemann surface. This result illustrates the sharpness of the Ehrenpreis conjecture.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00039-013-0211-1DOIArticle
http://link.springer.com/article/10.1007/s00039-013-0211-1PublisherArticle
http://arxiv.org/abs/1202.5780arXivDiscussion Paper
Additional Information:© 2013 Springer Basel. Received: March 14, 2012. Revised: January 25, 2013. Accepted: January 27, 2013. Published online March 7, 2013.
Issue or Number:3
Record Number:CaltechAUTHORS:20130730-113506238
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130730-113506238
Official Citation:Fletcher, A., Kahn, J. & Markovic, V. Geom. Funct. Anal. (2013) 23: 867. doi:10.1007/s00039-013-0211-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39657
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2013 20:11
Last Modified:03 Oct 2019 05:09

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