PLURIPOTENTIAL THEORY ON TEICHMULLER SPACE I: PLURICOMPLEX GREEN FUNCTION

This is the first paper in a series of investigations of the pluripotential theory on Teichmuller space. One of the main purposes of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichmuller space. We also show that Teichmuller space carries a natural stratified structure of real-analytic submanifolds defined from the structure of singularities of the initial differentials of the Teichmuller 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 Dumas' symplectic structure on the space of holomorphic quadratic differentials.