Year: 2024
Type: article
Abstract: In this paper, we discuss the boundary behavior of bounded pluriharmonic functions and bounded holomorphic 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.
DOI: 10.1093/imrn/rnae222
Author: Hideki Miyachi
Institution: Kanazawa University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403205456