Pluripotential theory on Teichm\"uller space II -- Poisson integral formula
Complex Variables
2022-12-26 v3 Geometric Topology
Abstract
This is the second paper in a series of investigations of the pluripotential theory on Teichm\"uller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on Teichm\"uller space which are continuous on the Bers compactification. We also observe that the Schwarz type theorem on the boundary behavior of the Poisson integral. We will see a relationship between the pluriharmonic measures and the Patterson-Sullivan measures discussed by Athreya, Bufetov, Eskin and Mirzakhani.
Keywords
Cite
@article{arxiv.1810.04343,
title = {Pluripotential theory on Teichm\"uller space II -- Poisson integral formula},
author = {Hideki Miyachi},
journal= {arXiv preprint arXiv:1810.04343},
year = {2022}
}
Comments
49 pages, 4 figures. In version 3, I revised typos, Introduction and add an application and an example