8 citations · 26 across the 15 of their papers we have counts for
17 papers
Sovability of curvature equations with multiple singular sources on torus via Painleve VI equations
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
We study the curvature equation with multiple singular sources on a torus \[Δu+e^{u}=8π\sum_{k=0}^{3}n_{k}δ_{\frac{ω_{k}}{2}}% +4π\left( δ_{p}+δ_{-p}\right) \quad \text{ on }\;E_τ:…
Sharp results for spherical metric on flat tori with conical angle 6 at two symmetric points
Ting-Jung Kuo
In this paper, we investigate the following curvature equation: \begin{equation} Δu+e^{u}=8π(δ_{0}+δ_{\frac{ω_{k}}{2}})\text{ in } E_{τ}\text{, }τ\in \mathbb{H} (0.1) \label{a} \en…
Proof of a conjecture of Dahmen and Beukers on counting integral Lamé equations with finite monodromy
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, we prove Dahmen and Beukers' conjecture that the number of integral Lamé equations with index modulo scalar equivalence with the monodromy group dihedral …
The geometry of generalized Lame equation, III: One-to-one of the Riemann-Hilbert correspondence
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, the third in a series, we continue to study the generalized Lamé equation H with the Darboux-Treibich-Verdier potential \begin{equation*} y^{\pr…
Blow up at infinity in the SU(3) Chern-Simons model, part I
Ting-Jung Kuo, Youngae Lee, Chang-Shou Lin
We consider non-topological solutions of a nonlinear elliptic system problem derived from the Chern-Simons models in . The existence of non-topological soluti…
On the CR analogue of Frankel conjecture and a smooth representative of the first Kohn-Rossi cohomology group
Der-Chen Chang, Shu-Cheng Chang, Ting-Jung Kuo +1
In this note, we first give a criterion of pseudo-Einstein contact forms and then affirm the CR analogue of Frankel conjecture in a closed, spherical, strictly pseudoconvex CR mani…
Global existence and convergence for the CR Q-curvature flow in a closed strictly pseudoconvex CR 3-manifold
Shu-Cheng Chang, Ting-Jung Kuo, Takanari Saotome
In this note, we affirm the partial answer to the long open Conjecture which states that any closed embeddable strictly pseudoconvex CR -manifold admits a contact form with…
The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, the second in a series, we continue to study the generalized Lamé equation with the Treibich-Verdier potential \begin{equation*} y^{\prime \prime }(z)=\bigg[ \sum_{k…
Pseudo-Einstein structure, eigenvalue estimate for the CR Paneitz operator and its applications to uniformization theorem
Shu-Cheng Chang, Ting-Jung Kuo, Chien Lin
In this note, we mainly focus on the existence of pseudo-Einstein contact forms, an upper bound eigenvalue estimate for the CR Paneitz operator and its applications to the uniformi…
The geometry of generalized Lamé equation, I
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, we prove that the spectral curve of the generalized Lamé equation with the Treibich-Verdier potential \begin{equation*} y^{\prime \prime }(z)=\bigg[…
Simple zero property of some holomorphic functions on the moduli space of tori
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
We prove that some holomorphic functions on the moduli space of tori have only simple zeros. Instead of computing the derivative with respect to the moduli parameter , we introd…
Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin +1
We study the spectral polynomial of the Treibich-Verdier potential. Such spectral polynomial, which is a generalization of the classical Lame polynomial, plays fundamental roles in…
On reducible monodromy representations of some generalized Lamé equation
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin +1
In this note, we compute the explicit formula of the monodromy data for a generalized Lamé equation when its monodromy is reducible but not completely reducible. We also solve the…
Non-existence of solutions for a mean field equation on flat tori at critical parameter
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
It is known from \cite{LW} that the solvability of the mean field equation with on a flat torus essentially depends on the geome…
Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, we study the Painlevé VI equation with parameter . We prove (i) An explicit formula to count the number of poles…
Hamiltonian system for the elliptic form of Painlevé VI equation
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In literature, it is known that any solution of Painlevé VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on . In this paper…
CR Sub-Laplacian Comparison and Liouville-type Theorem in a Complete Noncompact Sasakian Manifold
Shu-Cheng Chang, Ting-Jung Kuo, Chien Lin +1
In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e. Sasakian manifold). Secondly, we de…