Pluripotential theory on Teichmüller space I -- Pluricomplex Green function

Abstract

This is the first paper in a series of investigation of the pluripotential theory on Teichmüller space. The main purpose of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichmüller space. We also show that Teichmüller space carries a natural stratified structure of real-analytic submanifolds defined from the structure of singularities of the initial differentials of the Teichmüller mappings from a given point. We will also give a description of the Levi form of the pluricomplex Green function using the Thurston symplectic form via the Dumas symplectic structure on the space of holomorphic quadratic differentials.

30 pages, 2 figures. In the version 2, I revised typos, and add a proof of Proposition 6.2