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$ C^1$ estimates for the Weil-Petersson metric

Authors: Georgios Daskalopoulos and Chikako Mese
Journal: Trans. Amer. Math. Soc. 369 (2017), 2917-2950
MSC (2010): Primary 53C43; Secondary 32G15
Published electronically: December 7, 2016
MathSciNet review: 3592533
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Abstract: We prove that the Weil-Petersson metric near the boundary of the Teichmüller space is $ C^1$-asymptotically a product of the Weil-Petersson metric on a lower dimensional Teichmüller space and a metric on a model space. In particular, we show that the Weil-Petersson metric on the genus $ g$, $ p$-punctured Teichmüller space with $ 3g-3+p >0$ satisfies all the important properties required to apply the results in a previous work by the authors (2011). These estimates extend the well known $ C^0$ estimates for the Weil-Petersson metric.

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Additional Information

Georgios Daskalopoulos
Affiliation: Department of Mathematics, Brown University, P.O. Box 1917, Providence, Rhode Island 02912

Chikako Mese
Affiliation: Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218-2608

Received by editor(s): March 24, 2015
Received by editor(s) in revised form: May 6, 2015, and November 12, 2015
Published electronically: December 7, 2016
Additional Notes: The first author was supported by research grant NSF DMS-1308708
The second author was supported by research grant NSF DMS-1406332
Article copyright: © Copyright 2016 American Mathematical Society

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