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The Weil–Petersson and Takhtajan–Zograf metrics on the Riemann moduli spaces of complex structures for an n-fold punctured oriented surface of genus g, in the stable range g + 2n > 2, are shown here to have complete asymptotic expansions in terms of Fenchel–Nielsen coordinates at the exceptional divisors of the Knudsen–Deligne–Mumford compactification. This is accomplished by finding a full expansion for the hyperbolic metrics on the fibres of the universal curve as they approach the complete metrics on the nodal curves above the exceptional divisors and then using a push-forward theorem for conormal densities. This refines a two-term expansion due to Obitsu–Wolpert for the conformal factor relative to the model plumbing metric which in turn refined the bound obtained by Masur. A similar expansion for the Ricci metric is also obtained.

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Melrose, Richard B -  Zhu, Xuwen - 

Id.: 71341001

Versión: 1.0

Estado: Final

Tipo de recurso: Article  -  http://purl.org/eprint/type/JournalArticle  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Creative Commons Attribution-Noncommercial-Share Alike

Requerimientos técnicos:  Browser: Any - 

Relación: [IsBasedOn] arXiv
[References] http://dx.doi.org/10.1093/IMRN/RNX264
[References] International Mathematics Research Notices

Fecha de contribución: 27-may-2018


* 1073-7928
* 1687-0247
* Melrose, Richard and Xuwen Zhu. “Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces.” International Mathematics Research Notices (November 2017): 1-54 © 2017 The Authors

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