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arXiv · 2312.13535

Bounded pluriharmonic functions and holomorphic functions on Teichmüller space

Hideki Miyachi
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Abstract

In this paper, we discuss the boundary behavior of bounded pluriharmonic functions on the Teichmüller space. We will show a version of the Fatou theorem that every bounded pluriharmonic function admits the radial limits along the Teichmüller geodesic rays, and a version of the F. and M. Riesz theorem that the radial limit of a non-constant bounded holomorphic function is not constant on any non-null measurable set on the Bers boundary in terms of the pluriharmonic measure. As a corollary, we obtain the non-ergodicity of the action of the Torelli group for a closed surface of genus $g\ge 2$ on the space of projective measured foliations.

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Hideki Miyachi. 2024-09-16. Bounded pluriharmonic functions and holomorphic functions on Teichmüller space. https://arxiv.org/abs/2312.13535

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