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Harmonic maps and wild Teichmüller spaces

Gupta, S (2021) Harmonic maps and wild Teichmüller spaces. In: Journal of Topology and Analysis, 13 (2). pp. 349-393.

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Official URL: https://doi.org/10.1142/S1793525320500156


We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has noncompact ends with boundary cusps. This extends Wolf's parametrization of the Teichmüller space of a closed surface using holomorphic quadratic differentials. Our proof involves showing the existence of a harmonic map from a punctured Riemann surface to a crowned hyperbolic surface, with prescribed principal parts of its Hopf differential which determine the geometry of the map near the punctures.

Item Type: Journal Article
Publication: Journal of Topology and Analysis
Publisher: World Scientific
Additional Information: The copyright for this article belongs to the Authors.
Keywords: crowned hyperbolic surfaces; harmonic maps; Meromorphic quadratic differentials
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 16 May 2023 09:40
Last Modified: 16 May 2023 09:40
URI: https://eprints.iisc.ac.in/id/eprint/81681

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