Bounded Pluriharmonic Functions and Holomorphic Functions on Teichm\"uller Space II -- Poisson integral formula --
Abstract
In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichm\"uller space of analytically finite Riemann surfaces of type (g,m) with 2g-2+m>0. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichm\"uller space, as well as a Teichm\"uller-theoretic interpretation of the mean value theorem for pluriharmonic functions.
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