Miyachi Hideki

ミヤチヒデキ | Miyachi Hideki

Affiliation and department：

Research field (1)： Basic analysis

Research keywords (8)： Riemann surface , Moduli space , Quasiconformal mappings , Hyperbolic geometry , Discrete group , Teichmuller space , Complex analysis , Pluripotential theory

Research theme for competitive and other funds (22)：

2022 - 2027 3次元トポロジーへの応用を目指した離散群の表現空間と大域幾何の研究
2020 - 2026 Reconstructing the Thurston theory based on Higgs bundles and its new development
2020 - 2025 タイヒミュラー空間論の複素解析的側面の深化と多角的視点からの新展開
2018 - 2023 Various evolutions of Teichmuller theory
2017 - 2022 Geometry of discrete groups and its applications to 3-dimensional topology

2016 - 2021 Degeneration and collapsing of Kleinian groups; geometry and analysis of the compactification of their defamation spaces

2016 - 2019 Remodelling Kleinin group theory using ergodic theory and complex analysis

2016 - 2019 タイヒミュラー空間の複素解析的構造の研究

2011 - 2016 Teichmuller space and its topological dynamics via flat singular metrics on a surface

2010 - 2016 Global geometric studies on Kleinian groups and Teichmuller spaces

2010 - 2015 Geometric structure and combinatorial structure of 3-dimensional manifolds

2010 - 2014 Ergodic-theoretical study of dynamical systems and stochastic processes related to the theory of Teichmuller spaces

2011 - 2013 New development of the research of Lefschetz fibrations by Teichmuller theory

2009 - 2013 タイヒミュラー空間及びクライン群の変形空間の複素解析的構造の研究

2010 - 2012 Applications of global coordinate systems for the representation spaces of punctured surface groups

2008 - 2012 Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups

2007 - 2010 Global construction of pleating coordinates of Teichmuller spaces and its applications

2006 - 2010 Euclidean cone structures on a surface and Teichmuller spaces

2006 - 2009 Heegaard structures and geometric structures of 3-manifolds

2005 - 2008 A classification of hyperbolic 3-manifolds and deformation spaces of hyperbolic structures

2005 - 2007 タイヒミュラー空間とクライン群の変形空間の複素解析的構造の研究

2000 - 2002 タイヒミュラー空間の複素解析的埋めこみの解析的及び幾何学的性質の研究

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Papers (45)：

Hideki Miyachi. Pluripotential theory on Teichmüller space II - Poisson integral formula. Advances in Mathematics. 2023. 432. 109265-109265
Guangming Hu, Zhiyang Lv, Hideki Miyachi, Yi Qi, Dong Tan. The universal commensurability Busemann horofunction compactified Teichmüller space. Mathematische Nachrichten. 2023. 296. 8. 3375-3386
Guangming Hu, Hideki Miyachi. Estimates of the Bergman kernel on Teichmüller space. Proceedings of the American Mathematical Society. 2023. 151. 7. 2895-2905
Hideki Miyachi, Ken'ichi Ohshika, Athanase Papadopoulos. Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric. Annales Fennici Mathematici. 2022. 47. 1. 325-334
MIYACHI Hideki. Pluripotential theory on Teichmüller space I: Pluricomplex Green function. Conformal geometry and Dynamics. 2019. 23. 221-259

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MISC (4)：

MIYACHI HIDEKI. THURSTON THEORY ON TEICHMULLER SPACE WITH EXTREMAL LENGTH (Geometry of Moduli Space of Low Dimensional Manifolds). RIMS Kokyuroku. 2013. 1862. 20-29
MIYACHI HIDEKI. A SURVEY ON THE EXTREMAL LENGTH GEOMETRY ON TEICHMULLER SPACE (Geometric and analytic approaches to representations of a group and representation spaces). RIMS Kokyuroku. 2012. 1777. 50-56
Miyachi Hideki. On cusps in the boundary of the one-dimensional Teichmuller space (Hyperbolic Spaces and Related Topics II). RIMS Kokyuroku. 2000. 1163. 18-23
Miyachi Hideki. On cusps in the boundary of the Maskit slice for once puctured torus groups (Comprehensive Research on Complex Dynamical Systems and Related Fields). RIMS Kokyuroku. 2000. 1153. 20-28

Lectures and oral presentations (45)：

Towards Complex analysis on Teichmueller space
(International Conference on Complex Analysis 2019 2019)
Towards Complex analysis and Pluripotential theory on Teichmuller space
(2019)
Complex Analysis on Teichmüller space
(HAYAMA Symposium on Complex Analysis in Several Variables XXI 2019)
Poisson integral formula for Teichmueller space
(Riemann surfaces and Teichmuller theory 2019)
Toward Complex analysis on Teichmueller space
(Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry 2019)

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Awards (2)：

2021/09 - The mathematical society of Japan Analysis prize Study on complex analysis on Teichmüller space
2014 - 大阪大学総長奨励賞(研究部門)

Association Membership(s) (1)：

THE MATHEMATICAL SOCIETY OF JAPAN

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