MIYACHI Hideki

J-GLOBAL         Last updated: Dec 24, 2019 at 22:39
 
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Name
MIYACHI Hideki
Affiliation
Kanazawa University
Section
Institute of Science and Engineering Faculty of Mathematics and Physics
ORCID ID
0000-0003-4318-9539

Published Papers

 
MIYACHI Hideki
Conformal geometry and Dynamics   23 221-259   Nov 2019   [Refereed]
This is the first paper in a series of investigations of the pluripotential theory on Teichmüller space. One of the main purposes of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichm...
MIYACHI Hideki, Dragomir Saric
Proceedings of the American Mathematical Society   147(11) 4877-4899   2019   [Refereed]
We show that any Teichmuller disk in the universal Teichmuller space extends as a closed disk in the Thurston bordification.
Hideki Miyachi
Proc. Amer. Math. Soc.   147(1) 215-227   2019   [Refereed]
In this paper, we discuss the structure of the infinitesimal spaces of generic quasiconformal mappings. One of the main results is that for any countable set in the complex plane, the infinitesimal spaces of generic Tex-quasiconformal mappings at...
Hideki Miyachi
Handbook of group actions   III 3-12   2018   [Refereed]
Hideki Miyachi, Ken'ichi Ohshika
Annales Mathematiques Blaise Pascal.   24 115-133   2017   [Refereed]
For a piecewise linear path in the measured lamination space on a hyperbolic surface, we shall prove a differential formula of the extremal length function expressed by the intersection number. We shall also present two applications of this formul...
Vincent Alberge, Hideki Miyachi and Ken'ichi Ohshika
Handbook of Teichmuller Theory   VI 71-94   2017   [Refereed]
Hideki Miyachi
Tradition of Ahlfors_Bers, VII, Contemporary mathematics   696 225-250   2017   [Refereed]
In this paper, we show that the extremal length functions on Teichmuller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of Liu and Su’s result on the plurisubharmonicity of extremal length functions. We also obtain ...
Hideki Miyachi
Journal of Mathematical Society of Japan   69 995-1049   2017   [Refereed]
This paper is devoted to studying transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We characte...
Hideki Miyachi
Proceedings of the Japan Academy, Series A, Mathematical Sciences   91(10) 151-154   2015   [Refereed]
In this paper, we give a rigidity theorem for holomorphic disks associated to holomorphic families of Riemann surfaces, aiming for studying the geometry (the asymptotic boundary behaviors) of such holomorphic disks. Indeed, our rigidity theorem is...
Hideki Miyachi
Proceedings of American Mathematical Society   143 2949-2957   2015   [Refereed]
Abstract: In this paper, we discuss a rigidity property for holomorphic disks in Teichmuller space. In fact, we give an improvement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds...

Conference Activities & Talks

 
Towards Complex analysis on Teichmueller space [Invited]
MIYACHI Hideki
International Conference on Complex Analysis 2019   18 Sep 2019   
I discuss the Poisson integral formula on Teichmuller space.
MIYACHI Hideki
6 Sep 2019   
I give two talks. In the first talk, I discuss the background of Teichmuller theory. In the second talk, I give a proof (sketch) of the proofs on the Kruchkal formula for the pluricomplex Green function and the pluriharmonic measures.
MIYACHI Hideki
HAYAMA Symposium on Complex Analysis in Several Variables XXI   13 Jul 2019   
In this talk, I discuss the Poisson integral formula for Bers slice.
MIYACHI Hideki
Riemann surfaces and Teichmuller theory   8 Jul 2019   
In this talk we give an explicit form on the Poisson integral formula on the Bers slice.
Hideki Miyachi
Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry   26 Mar 2019   
In this talk we give an explicit form on the Poisson integral formula on the Bers slice.
Hideki Miyachi
2018年度「リーマン面・不連続群論」研究集会   9 Feb 2019   
In this talk we give an explicit form on the Poisson integral formula on the Bers slice
Toward Complex analysis with Thurston theory [Invited]
Hideki Miyachi
RIMS 共同研究(公開型)『複素力学系研究とその発展』(Complex dynamical systems and related topics)   10 Dec 2018   
In this talk we give an explicit form on the Poisson integral formula on the Bers slice
Hideki Miyachi
New Trends in Teichmuller Theory and Mapping Class Groups   2 Sep 2018   
タイヒミュラー空間の複素構造に関する自身の研究成果を発表した.ベアスコンパクト化で定義される多重調和函数に対するポアソン積分表示を発表した.
Teichmuller theory and shear coordinates [Invited]
Hideki Miyachi
研究集会「モジュライ空間のシンプレクティック幾何」   26 Jan 2018   
タイヒミュラー空間のShear座標系について説明した
Hideki Miyachi
2017年度多変数関数論冬セミナー   24 Dec 2017   
タイヒミュラー空間の複素解析学的理論と位相幾何学的理論の統一的解釈に関する研究の進展状況を講演した.

Association Memberships