Katsuhiko Matsuzaki

collaborators

10 papers

math.CV2026

$BMO$ Domains and Quasicircles Associated with Zygmund Functions

Katsuhiko Matsuzaki, Fei Tao

We investigate graph domains and graph curves from the viewpoints of $BMOA$ , Zygmund regularity, and asymptotic geometry. First, we prove that every graph domain is a $\ma…

math.CV2026

Weak Asymptotic Symmetry of Quasisymmetric Embeddings on Quasilines

Katsuhiko Matsuzaki, Fei Tao

We investigate the relationship between weak asymptotic symmetry ( $WAS$ ) and asymptotic symmetry ( $AS$ ) for quasisymmetric maps associated with planar quasilines.…

math.CO2026

A Conway-Coxeter theorem for decorated frieze patterns

Takeru Kuwana, Katsuhiko Matsuzaki

Let $m \geq 0$ and put $n = m + 3$ . We introduce a normalized positive Laurent class of decorated frieze patterns and prove a decorated analogue of the Conway-Coxeter classification theo…

math.CV2026

Graph Weldings Associated with Functions in Zygmund, $BMO$ , $VMO$ , and $H^{1/2}$

Katsuhiko Matsuzaki, Fei Tao

Let $f : R \to R$ be a continuous function. We define the graph welding associated with $f$ as the homeomorphism \[ φ= G^{-1}\circ F\colon \mathbb{R}\to\mathbb{…

math.CV2026

Boundary Characterizations of Little Bloch and $VMOA$ Functions on the Half-Plane

Katsuhiko Matsuzaki, Fei Tao

We extend Pommerenke's characterizations of boundary curves of conformal mappings in terms of the little Bloch and $VMOA$ conditions from the unit disk $D$ to the…

math.CV2025

Characterization of Asymptotically Smooth Chord-arc Curves

Katsuhiko Matsuzaki, Fei Tao

We construct an explicit example of an asymptotically conformal chord-arc curve that fails to be asymptotically smooth. This implies that a function belonging to both the little Bl…

math.CV2025

Integrable Teichmüller spaces for analysis on Weil-Petersson curves

Katsuhiko Matsuzaki

The integrableTeichmüller space $T_{p}$ for $p \geq 1$ is defined by the $p$ -integrability of Beltrami coefficients. We characterize a quasisymmetric homeomorphism $h$ in $T_{p}$ by th…

math.GT2025

Handlebodies of Infinite Genus and Schottky Groups

Ara Basmajian, Katsuhiko Matsuzaki

In this paper, we begin an investigation of infinite genus handlebodies, infinitely generated Schottky groups, and related uniformization questions by giving appropriate definition…

math.CO2025

Arithmetic Y-frieze patterns of width 3 and 4

Katsuhiko Matsuzaki, Taiki Resnick

We determine all arithmetic Y-Frieze patterns of width $3$ and $4$ . As a consequence, for $n = 3, 4$ , we verify the surjectivity of a map $p_{n}$ which corresponds arithmetic Y-Frieze p…

math.CV2025

Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces

Katsuhiko Matsuzaki

On two subsurfaces of a Riemann surface divided by a $p$ -Weil-Petersson curve $γ$ , we consider the spaces of harmonic functions whose $p$ -Dirichlet integrals are finite in the comp…

BMO Domains and Quasicircles Associated with Zygmund Functions

Weak Asymptotic Symmetry of Quasisymmetric Embeddings on Quasilines

A Conway-Coxeter theorem for decorated frieze patterns

Graph Weldings Associated with Functions in Zygmund, BMO, VMO, and H1/2

Boundary Characterizations of Little Bloch and VMOA Functions on the Half-Plane

Characterization of Asymptotically Smooth Chord-arc Curves

Integrable Teichmüller spaces for analysis on Weil-Petersson curves

Handlebodies of Infinite Genus and Schottky Groups

Arithmetic Y-frieze patterns of width 3 and 4

Weil-Petersson curves and Dirichlet finite harmonic functions on Riemann surfaces

$BMO$ Domains and Quasicircles Associated with Zygmund Functions

Graph Weldings Associated with Functions in Zygmund, $BMO$ , $VMO$ , and $H^{1/2}$

Boundary Characterizations of Little Bloch and $VMOA$ Functions on the Half-Plane