Gupta, S (2021) Harmonic maps and wild Teichmüller spaces. In: Journal of Topology and Analysis, 13 (2). pp. 349-393.
|
PDF
jou_top_ana_13-2_349-393_2021.pdf - Published Version Download (746kB) | Preview |
Abstract
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 |
Actions (login required)
 |
View Item |
