𝐶¹ estimates for the Weil-Petersson metric

Daskalopoulos, Georgios; Mese, Chikako

doi:10.1090/tran/6890

$C^1$ estimates for the Weil-Petersson metric
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by Georgios Daskalopoulos and Chikako Mese PDF

Trans. Amer. Math. Soc. 369 (2017), 2917-2950 Request permission

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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