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On asymptotic Teichmüller space

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Fletcher, A. (Alastair). (2010) On asymptotic Teichmüller space. American Mathematical Society. Transactions, Vol.362 (No.5). pp. 2507-2523. ISSN 0002-9947

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Official URL: http://dx.doi.org/10.1090/S0002-9947-09-04944-7

Abstract

In this article we prove that for any hyperbolic Riemann surface M of infinite analytic type, the little Bers space Q0(M) is isomorphic to c0. As a consequence of this result, if M is such a Riemann surface, then its asymptotic Teichm¨uller space AT(M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l∞/c0. Further, if M and N are two such Riemann surfaces, their asymptotic Teichm¨uller spaces, AT(M) and AT(N), are locally bi-Lipschitz equivalent

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Teichmüller spaces, Riemann surfaces, Banach spaces
Journal or Publication Title:	American Mathematical Society. Transactions
Publisher:	American Mathematical Society
ISSN:	0002-9947
Date:	2010
Volume:	Vol.362
Number:	No.5
Page Range:	pp. 2507-2523
Identification Number:	10.1090/S0002-9947-09-04944-7
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/3390