2023/12/21 by Hideki Miyachi, Miyachi, Hideki · 1 citation
Mathematics · #32G05 #32G15 #32U35 #57M50 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2312.13535
openalex publication_date 2023/12/21 · openalex created_date 2023/12/23 · openalex updated_date 2026/07/28
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≥ 2 on the space of projective measured foliations.