Natsuo Miyatake

activity

20202025

most citedGeneralized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space

6 citations · 9 across the 10 of their papers we have counts for

collaborators

10 papers

math.DG2025

Complete harmonic metrics and subharmonic functions on the unit disc

Natsuo Miyatake

Let $X$ be a Riemann surface with canonical bundle $K_{X}$ and holomorphic tangent bundle $T_{X} = K_{X}^{- 1}$ . For each integer $r \geq 2$ , each $q \in H^{0} (K_{X}^{r})$ , and each choice of a squ…

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, $K_{X}$ its canonical bundle, and $T_{X} = K_{X}^{- 1}$ . A diagonal harmonic metric $h = (h_{1}, \dots, h_{r})$ on a cyclic Higgs bundle of rank $r \geq 2$ associated w…

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…

math.DG2023

Generalizations of Hermitian-Einstein equation of cyclic Higgs bundles, their heat equation, and inequality estimates

Natsuo Miyatake

We introduce some generalizations of the Hermitian-Einstein equation for diagonal harmonic metrics on cyclic Higgs bundles, including a generalization using subharmonic functions.…

math.DG2023

Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields

Natsuo Miyatake

We consider a Higgs bundle over a compact Kähler manifold with a smooth, non-holomorphic Higgs field. We assume that the holomorphic vector bundle decomposes into a direct sum of h…

math.DG2022★ 2 cited

Uniformizations of compact Sasakian manifolds

Hisashi Kasuya, Natsuo Miyatake

We give a criterion for compact Sasakian manifolds to be deformed to Sasakian manifolds which are locally isomorphic to circle bundles of anti-canonical bundles over Hermitian symm…

math.DG2022

Generalized Kazdan-Warner equations on foliated manifolds

Natsuo Miyatake

On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve,…

math.DG2021★ 1 cited

On diagonal pluriharmonic metrics of $G$ -Higgs bundles

Natsuo Miyatake

Let $(E, Φ) \to (X, ω_{X})$ be a Higgs bundle over a compact Kähler manifold. We suppose that the holomorphic vector bundle $E$ decomposes into a direct sum of holomorphic line…

math.DG2020★ 6 cited

Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space

Natsuo Miyatake

We introduce generalized Kazdan-Warner equations on Riemannian manifolds associated with a linear action of a torus on a complex vector space. We show the existence and the uniquen…

Complete harmonic metrics and subharmonic functions on the unit disc

Shannon entropy for harmonic metrics on cyclic Higgs bundles II

Shannon entropy for harmonic metrics on cyclic Higgs bundles

Cyclic Higgs bundles, subharmonic functions, and the Dirichlet problem

Generalizations of Hermitian-Einstein equation of cyclic Higgs bundles, their heat equation, and inequality estimates

Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields

Uniformizations of compact Sasakian manifolds

Generalized Kazdan-Warner equations on foliated manifolds

On diagonal pluriharmonic metrics of G-Higgs bundles

Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space

On diagonal pluriharmonic metrics of $G$ -Higgs bundles