2 citations · 4 across the 13 of their papers we have counts for
15 papers
On the Teichm{ü}ller space of acute triangles
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
We continue the study of the analogue of Thurston's metric on the Teichm{ü}ller space of Euclidean triangle which was started by Saglam and Papadopoulos in [1].By direct calculatio…
The Teichm{ü}ller-Randers metric
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
In this paper, we introduce a new asymmetric weak metric on the Teichm{ü}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call th…
Estimates of the Bergman kernel on Teichmuller space
Guangming Hu, Hideki Miyachi
In this paper, a comparison between the Bergman kernel form and the pushforward measure of the Masur-Veech meaure on the Teichmuller space of genus is obtained.
Tangent spaces of the Teichm{ü}ller space of the torus with Thurston's weak metric
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichm{ü}ller space of flat structures on the torus is weak Finsler and we give a geometric descript…
Universal commensurability augmented Teichmüller space and moduli space
Guangming Hu, Hideki Miyachi, Yi Qi
It is known that every finitely unbranched covering of a compact Riemann surface with genus induces an isometric embedding …
Pluripotential theory on Teichmüller space II -- Poisson integral formula
Hideki Miyachi
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 formul…
Pluripotential theory on Teichmüller space I -- Pluricomplex Green function
Hideki Miyachi
This is the first paper in a series of investigation of the pluripotential theory on Teichmüller space. The main purpose of this paper is to give an alternative approach to the Kru…
Convergence of Teichmüller deformations in the universal Teichmüller space
Hideki Miyachi, Dragomir Šarić
Let be an integrable holomorphic function on the unit disk and the Teichmüller disk in the universal Teic…
Extremal length functions are log-plurisubharmonic
Hideki Miyachi
In this paper, we show that the extremal length functions on Teichmüller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of L.Liu and W.Su's results…
A rigidity theorem for holomorphic disks in Teichmüller space
Hideki Miyachi
In this paper, we discuss a rigidity property for holomorphic disks in Teichmüller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigid…
Geometry of the Gromov product : Geometry at infinity of Teichmüller space
Hideki Miyachi
This paper is devoted to study of transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptot…
Unification of extremal length geometry on Teichmuller space via intersection number
Hideki Miyachi
In this paper, we give a framework for the study of the extremal length geometry of Teichmüller space after S. Kerckhoff, F. Gardiner and H. Masur. There is a natural compactificat…
Extremal length boundary of Teichmüller space contains non-Busemann points
Hideki Miyachi
In this paper, we shall show that the metric boundary of the Teichmueller space with respect to the Teichmueller distance contains non-Busemann points when the complex dimension of…
A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane
Hideki Miyachi, Dragomir Saric
We prove that the bijective correspondence between the space of bounded measured laminations and the universal Teichmüller space given by $λ\maps…
Gardiner-Masur boundary of Teichmuller space : Vanishing subsurfaces and Uniquely ergodic boundary points
Hideki Miyachi
In this paper, we investigate the structure of the Gardiner-Masur boundary of Teichmuller space. Indeed, we will give a geometric description of boundary comparing to the Duchin-Le…