Pollicott, Mark and Sharp, Richard (2016) Weil–Petersson metrics, Manhattan curves and Hausdorff dimension. Mathematische Zeitschrift, 282 (3-4). pp. 1007-1016. doi:10.1007/s00209-015-1575-8 ISSN 0025-5874.

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Abstract

In this note we want to relate the Weil-Petersson metric on Teichm¨uller space to the boundary correspondence between the actions on the boundary of Fuchsian groups. Consider the space of Riemann metrics g on a compact surface V with negative Euler characteristic. This can be endowed with a number of natural Riemannian metrics. Of particular interest is the Weil-Petersson metric, whose definition was proposed by Weil in 1958 based on earlier work of Petersson, cf. [18]. There is a particularly intuitive equivalent definition of the Weil-Petersson metric using the second derivative of lengths of typical (closed) geodesics due to Thurston and Wolpert [19].

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Metric spaces, Curves, Hausdorff measures
Journal or Publication Title:	Mathematische Zeitschrift
Publisher:	Springer
ISSN:	0025-5874
Official Date:	April 2016
Dates:	Date Event April 2016 Published 19 November 2015 Available 14 October 2015 Accepted 22 January 2014 Submitted
Volume:	282
Number:	3-4
Number of Pages:	10
Page Range:	pp. 1007-1016
DOI:	10.1007/s00209-015-1575-8
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	28 January 2016
Date of first compliant Open Access:	28 January 2016

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