Pluripotential theory on Teichmuller space II - Poisson integral formula

被引：1

作者：

Miyachi, Hideki ^{[1
]}

机构：

[1] Kanazawa Univ, Sch Math & Phys, Coll Sci & Engn, Kakuma Machi, Kanazawa, Ishikawa 9201192, Japan

来源：

ADVANCES IN MATHEMATICS | 2023年 / 432卷

关键词：

Teichmuller space; Teichmuller distance; Levi forms; Pluricomplex Green functions; Poisson integral formula; Thurston measure; GARDINER-MASUR BOUNDARY; HYPERBOLIC MANIFOLDS; RIEMANN SURFACES; MODULAR GROUP; GEODESICS; CLASSIFICATION; CONTINUITY; GEOMETRY; CURRENTS; GROWTH;

D O I：

10.1016/j.aim.2023.109265

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is the second paper in a series of investigations of the pluripotential theory on the Teichmuller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on the Teichmuller 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.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：64

共 15 条

[1] PLURIPOTENTIAL THEORY ON TEICHMULLER SPACE I: PLURICOMPLEX GREEN FUNCTION
Miyachi, Hideki
CONFORMAL GEOMETRY AND DYNAMICS, 2019, 23 : 221 - 250
[2] The pluripotential compactification of Teichmuller space
Jiang, Kaige
Liu, Peijia
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 494 (01)
[3] The Poisson boundary of Teichmuller space
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JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 156 (02) : 301 - 332
[4] Teichmuller rays and the Gardiner-Masur boundary of Teichmuller space II
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GEOMETRIAE DEDICATA, 2013, 162 (01) : 283 - 304
[5] Harmonic Mappings and Quasihomographies in the Theory of Teichmuller Space
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COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS IV, PT 1: FUNCTION THEORY AND OPTIMIZATION, 2011, 553 : 289 - 304
[6] Poisson structures on the Teichmuller space of hyperbolic surfaces with conical points
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IN THE TRADITION OF AHLFORS-BERS, V, 2010, 510 : 307 - 329
[7] Quantum Mechanical Correspondence of Poisson Integral Formula
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Jiang Nian-Quan
COMMUNICATIONS IN THEORETICAL PHYSICS, 2011, 55 (02) : 217 - 220
[8] Quantum Mechanical Correspondence of Poisson Integral Formula
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姜年权
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[9] Optimal Lipschitz maps on one-holed tori and the Thurston metric theory of Teichmuller space
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Papadopoulos, Athanase
GEOMETRIAE DEDICATA, 2021, 214 (01) : 465 - 488
[10] Brain morphometry on congenital hand deformities based on Teichmuller space theory
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Wang, Xu
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Frey, Scott H.
Gu, Xianfeng
COMPUTER-AIDED DESIGN, 2015, 58 : 84 - 91

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