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arXiv · 1905.02911

On A Fully Nonlinear Equation in Relativistic Teichmüller Theory

Leun-Fai Tam·Tom Yau-Heng Wan
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Abstract

We obtain basic estimates for a Monge-Ampère equation introduced by Moncrief in the study of the Relativistic Teichmüller Theory. We then give another proof of the parametrization of the Teichmüller space obtained by Moncrief. Our approach provides yet another proof of the classical Teichmüller theorem that the Teichmüller space of a compact oriented surface of genus $g(Σ)>1$ is diffeomorphic to the disk of dimension $6g(Σ)-6$. We also give another proof of properness of a certain energy function on the Teichmüller space.

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Leun-Fai Tam, Tom Yau-Heng Wan. 2019-05-08. On A Fully Nonlinear Equation in Relativistic Teichmüller Theory. https://arxiv.org/abs/1905.02911

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