Proceedings of the American Mathematical Society

Author(s): Jeffrey Brock; Dan Margalit
Journal: Proc. Amer. Math. Soc. 135 (2007), 795-803.
MSC (2000): Primary 32G15; Secondary 32M99
Posted: September 11, 2006
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Abstract: We extend a theorem of Masur-Wolf which states that given a finite-area hyperbolic surface

, every isometry of the Teichmüller space for

with the Weil-Petersson metric is induced by an element of the mapping class group for

. Our argument handles the previously untreated cases of the four times-punctured sphere, the once-punctured torus, and the twice-punctured torus.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32G15, 32M99

Jeffrey Brock
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Email: brock@math.brown.edu

Dan Margalit
Affiliation: Department of Mathematics, University of Utah, 155 S 1440 East, Salt Lake City, Utah 84112-0090
Email: margalit@math.utah.edu

DOI: 10.1090/S0002-9939-06-08577-7
PII: S 0002-9939(06)08577-7
Keywords: Teichm\"uller space, Weil--Petersson metric, isometries, mapping class groups
Received by editor(s): January 18, 2005
Received by editor(s) in revised form: October 14, 2005
Posted: September 11, 2006
Additional Notes: The first author was partially supported by NSF grant number 0354288.
The second author was partially supported by an NSF postdoctoral fellowship and a VIGRE postdoctoral position under NSF grant number 0091675 to the University of Utah.
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2006, American Mathematical Society

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