Teichmüller Theory, Thurston Theory, Extremal Length Geometry and Complex Analysis

Miyachi, Hideki

doi:10.1007/978-3-030-55928-1_13

Cited by 2 publications

(3 citation statements)

References 63 publications

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“…The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on Teichmüller space which are continuous on the Bers compactification. This result is announced in [56] and [57].…”

Section: Introductionmentioning

confidence: 71%

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Pluripotential theory on Teichmüller space II -- Poisson integral formula

Miyachi¹

2018

Preprint

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This is the second paper in a series of investigations of the pluripotential theory on Teichmüller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on Teichmüller space which are continuous on the Bers compactification. We also observe that the Schwarz type theorem on the boundary behavior of the Poisson integral. We will see a relationship between the pluriharmonic measures and the Patterson-Sullivan measures discussed by Athreya, Bufetov, Eskin and Mirzakhani.

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Section: Introductionmentioning

confidence: 71%

“…Actually, in the case of (g, m) = (1, 1), the formula (1.2) coincides with the classical Poisson integral formula after identifying the Bers compactification with the closed disk D = {|z| ≤ 1} such that the origin of D corresponds to the square torus (cf. [56] and [47,Theorem B]. See also Example in §14.2).…”

Section: Introductionmentioning

confidence: 98%

Pluripotential theory on Teichmüller space II -- Poisson integral formula

Miyachi¹

2018

Preprint

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“…The Krushkal formula (1.1) of the pluricomplex Green function plays a crucial rule in the second paper. This result is announced in [47].…”

Section: Introductionmentioning

confidence: 79%

Pluripotential theory on Teichmüller space I -- Pluricomplex Green function

Miyachi¹

2018

Preprint

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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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Teichmüller Theory, Thurston Theory, Extremal Length Geometry and Complex Analysis

Cited by 2 publications

References 63 publications

Pluripotential theory on Teichmüller space II -- Poisson integral formula

Pluripotential theory on Teichmüller space II -- Poisson integral formula

Pluripotential theory on Teichmüller space I -- Pluricomplex Green function

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