6 papers
Hopf decomposition of the actions of subgroups of the mapping class group
Hideki Miyachi
We study the Hopf decomposition of subgroup actions of the Teichmüller modular group on the Thurston boundary with respect to the Thurston measure class. We identify the conservati…
Function theory, Dynamics and Ergodic theory via Thurston theory
Hideki Miyachi
In this paper, we discuss function theory on Teichmüller space through Thurston's theory, as well as the dynamics of subgroups of the mapping class group of a surface, with referen…
Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --
Hideki Miyachi
In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichmüller space of analytically finite Riemann surfaces of type with $…
Benoist-Hulin groups
Hideki Miyachi, Yannian Zhao
A Benoist-Hulin group is, by definition, a subgroup of such that any -invariant closed set consisting of Jordan curves in the space of closed subse…
The --geometry of Teichmüller space -- Second order infinitesimal structures
Hideki Miyachi
The - geometry is the Finsler geometry of the Teichmüller space by the Teichmüller metric and the -norm function of holomorphic quadratic differentials. In this…
Bounded pluriharmonic functions and holomorphic functions on Teichmüller space
Hideki Miyachi
In this paper, we discuss the boundary behavior of bounded pluriharmonic functions on the Teichmüller space. We will show a version of the Fatou theorem that every bounded plurihar…