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arXiv · 1708.04780

Harmonic maps and wild Teichm\"uller spaces

Subhojoy Gupta
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Abstract

We use meromorphic quadratic differentials with higher order poles to parametrize the Teichm\"uller 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 non-compact ends with boundary cusps. This extends Wolf's parametrization of the Teichm\"uller 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.

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Subhojoy Gupta. 2017-08-16. Harmonic maps and wild Teichm\"uller spaces. https://arxiv.org/abs/1708.04780

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