English

Bounded Pluriharmonic Functions and Holomorphic Functions on Teichm\"uller Space II -- Poisson integral formula --

Complex Variables 2025-07-29 v1 Geometric Topology

Abstract

In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichm\"uller space of analytically finite Riemann surfaces of type (g,m)(g,m) with 2g2+m>02g-2+m>0. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichm\"uller space, as well as a Teichm\"uller-theoretic interpretation of the mean value theorem for pluriharmonic functions.

Keywords

Cite

@article{arxiv.2507.19930,
  title  = {Bounded Pluriharmonic Functions and Holomorphic Functions on Teichm\"uller Space II -- Poisson integral formula --},
  author = {Hideki Miyachi},
  journal= {arXiv preprint arXiv:2507.19930},
  year   = {2025}
}