Pluripotential theory on Teichmüller space II -- Poisson integral formula

Miyachi, Hideki

doi:10.48550/arxiv.1810.04343

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2018

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“…See §7.1 for the definition of the pluricomplex Green function. In the second paper [48], we will establish the Poisson integral formula for pluriharmonic functions on Teichmüller space which are continuous on the Bers compactification. The Krushkal formula (1.1) of the pluricomplex Green function plays a crucial rule in the second paper.…”

Section: Introductionmentioning

confidence: 99%

Pluripotential theory on Teichmüller space I -- Pluricomplex Green function

Miyachi¹

2018

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This is the first paper in a series of investigations of the pluripotential theory on Teichmüller space. One of 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 Dumas' symplectic structure on the space of holomorphic quadratic differentials.

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Section: Introductionmentioning

confidence: 99%