Natsuo Miyatake

activity

20232025

collaborators

4 papers

math.DG2025

Complete harmonic metrics and subharmonic functions on the unit disc

Natsuo Miyatake

Let $X$ be a Riemann surface, $K_{X} \to X$ the canonical bundle, and $T_{X} \to X$ the dual bundle of the canonical bundle. For each integer $r \geq 2$ , each $q \in H^0…

math.DG2025

Shannon entropy for harmonic metrics on cyclic Higgs bundles II

Natsuo Miyatake

Let $X$ be a Riemann surface and $K_{X} \to X$ the canonical bundle. For each integer $r \geq 2$ , each $q \in H^{0} (K_{X}^{r})$ , and each choice of the square root $K_{X}^{1/2}$ of t…

math.DG2024

Shannon entropy for harmonic metrics on cyclic Higgs bundles

Natsuo Miyatake

Let $X$ be a Riemann surface, $K_{X} \to X$ the canonical bundle, and $T_{X} = K_{X}^{- 1} \to X$ the dual bundle of the canonical bundle. For each integer $r \geq 2$ , each…

math.DG2023

Cyclic Higgs bundles, subharmonic functions, and the Dirichlet problem

Natsuo Miyatake

We demonstrate the existence and uniqueness of the solution to the Dirichlet problem for a generalization of Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundle…