$C^1$ estimates for the Weil-Petersson metric
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- by Georgios Daskalopoulos and Chikako Mese PDF
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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.References
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Additional Information
- Georgios Daskalopoulos
- Affiliation: Department of Mathematics, Brown University, P.O. Box 1917, Providence, Rhode Island 02912
- MR Author ID: 313609
- Email: daskal@math.brown.edu
- Chikako Mese
- Affiliation: Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218-2608
- MR Author ID: 641800
- Email: cmese@math.jhu.edu
- 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 - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2917-2950
- MSC (2010): Primary 53C43; Secondary 32G15
- DOI: https://doi.org/10.1090/tran/6890
- MathSciNet review: 3592533