Pluripotential theory on Teichmüller space II – Poisson integral formula

Abstract

This is the second paper in a series of investigations of the pluripotential theory on the Teichmüller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on the Teichmüller 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.