Gupta, S (2019) Limits of harmonic maps and crowned hyperbolic surfaces. In: Transactions of the American Mathematical Society, 372 (11). pp. 7573-7596.
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Abstract
We consider harmonic diffeomorphisms to a fixed hyperbolic target Y from a family of domain Riemann surfaces degenerating along a Teichmüller ray. We use the work of Minsky to show that there is a limiting harmonic map from the conformal limit of the Teichmüller ray to a crowned hyperbolic surface. The target surface is the metric completion of the complement of a geodesic lamination on Y . The conformal limit is obtained by attaching half-planes and cylinders to the critical graph of the holomorphic quadratic differential determining the ray. As an application, we provide a new proof of the existence of harmonic maps from any punctured Riemann surface to a given crowned hyperbolic target of the same topological type.
| Item Type: | Journal Article |
|---|---|
| Publication: | Transactions of the American Mathematical Society |
| Publisher: | American Mathematical Society |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 12 Oct 2022 09:13 |
| Last Modified: | 12 Oct 2022 09:13 |
| URI: | https://eprints.iisc.ac.in/id/eprint/77398 |
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