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Meromorphic quadratic differentials and measured foliations on a Riemann surface

Gupta, Subhojoy and Wolf, Michael (2019) Meromorphic quadratic differentials and measured foliations on a Riemann surface. In: MATHEMATISCHE ANNALEN, 373 (1-2). pp. 73-118.

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Official URL: https://dx.doi.org/10.1007/s00208-018-1674-z

Abstract

We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential q if we prescribe, in addition, the principal parts of root q at the poles. This generalizes a theorem of Hubbard and Masur for holomorphic quadratic differentials. The proof analyzes infinite-energy harmonic maps from the Riemann surface to R-trees of infinite co-diameter, with prescribed behavior at the poles.

Item Type: Journal Article
Additional Information: The copyright for this article belongs to Springer New York LLC
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Ms Ranganayaki RS
Date Deposited: 14 May 2019 12:23
Last Modified: 14 May 2019 12:23
URI: http://eprints.iisc.ac.in/id/eprint/62677

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