THE GREEN-FUNCTION OF TEICHMULLER-SPACES WITH APPLICATIONS

We describe briefly a new approach to some problems related to Teichmuller spaces, invariant metrics, and extremal quasiconformal maps. This approach is based on the properties of plurisubharmonic functions, especially of the plurisubharmonic Green function. The main theorem gives an explicit representation of the Green function for Teichmuller spaces by the Kobayashi-Teichmuller metric of these spaces. This leads to various applications. In particular, this gives a new characterization of extremal quasiconformal maps.