Hideki Miyachi

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math.CV2025

Function theory, Dynamics and Ergodic theory via Thurston theory

Hideki Miyachi

In this paper, we discuss function theory on TeichmÃ¼ller space through Thurston's theory, as well as the dynamics of subgroups of the mapping class group of a surface, with refere…

math.CV2025

Bounded Pluriharmonic Functions and Holomorphic Functions on TeichmÃ¼ller Space II -- Poisson integral formula --

Hideki Miyachi

In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the TeichmÃ¼ller space of analytically finite Riemann surfaces of type $(g, m)$ with…

math.CV2024

Bounded pluriharmonic functions and holomorphic functions on TeichmÃ¼ller space

Hideki Miyachi

In this paper, we discuss the boundary behavior of bounded pluriharmonic functions on the TeichmÃ¼ller space. We will show a version of the Fatou theorem that every bounded pluriha…

math.CV2024

The $L^{1}$ - $L^{\infty}$ -geometry of TeichmÃ¼ller space -- Second order infinitesimal structures

Hideki Miyachi

The $L^{1}$ - $L^{\infty}$ geometry is the Finsler geometry of the TeichmÃ¼ller space by the TeichmÃ¼ller metric and the $L^{1}$ -norm function of holomorphic quadratic differentials. In th…

Function theory, Dynamics and Ergodic theory via Thurston theory

Bounded Pluriharmonic Functions and Holomorphic Functions on TeichmÃ¼ller Space II -- Poisson integral formula --

Bounded pluriharmonic functions and holomorphic functions on TeichmÃ¼ller space

The L1-L∞-geometry of TeichmÃ¼ller space -- Second order infinitesimal structures

The $L^{1}$ - $L^{\infty}$ -geometry of TeichmÃ¼ller space -- Second order infinitesimal structures