Meromorphic quadratic differentials and measured foliations on a Riemann surface

Subhojoy Gupta; Michael Wolf

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arXiv · 1612.08043

Meromorphic quadratic differentials and measured foliations on a Riemann surface

Subhojoy Gupta·Michael Wolf

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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 $\sqrt q$ 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 $\mathbb{R}$-trees of infinite co-diameter, with prescribed behavior at the poles.

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Subhojoy Gupta, Michael Wolf. 2016-12-23. Meromorphic quadratic differentials and measured foliations on a Riemann surface. https://arxiv.org/abs/1612.08043

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