Erjuan Fu

activity

20202026

most citedA necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in

R

1 citations · 2 across the 9 of their papers we have counts for

collaborators

10 papers

math.AP2026

Geometric analysis on rhombus torus: Green function with two singularities

Zhijie Chen, Erjuan Fu, Chang-Shou Lin +1

Let $G (z)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ has at m…

math.AP2026

Classification of spherical metrics on tori with four singularities, I: half periods

Erjuan Fu, Chang-Shou Lin

Classifying the spherical metrics on a torus $E_{τ}$ with $4 π$ conic angle at each half period point\, $ω_{k} / 2, k = 0, 1, 2, 3$ \, is equivalent to classify solutions of the following c…

math.CA2026

On monodromy and spectral geometry of generalized Lamé equations with four singularities, I: half periods

Erjuan Fu, Chang-Shou Lin

We consider the unitary monodromy problem of the following generalized Lamé equations with apparent parameters \begin{equation*} y^{\prime\prime}(z)=\left(\frac{3}{4}\sum_{k=0}^3\w…

math.AP2025

Green functions, Hitchin's formula and curvature equations on tori II: Rectangular torus

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $G (z)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ has eith…

math.AP2025

Green functions, Hitchin's formula and curvature equations on tori

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $G (z) = G (z; τ)$ be the Green function on the flat torus $E_{τ} = C / (Z + Z τ)$ with the singularity at $0$ . Lin and Wang (Ann. Math. 2010) proved that $G (z)$ h…

math.AP2025

Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

Let $E_{τ} := C / (Z + Z τ)$ with $Im τ > 0$ be a flat torus and $G (z; τ)$ be the Green function on $E_{τ}$ with the singularity at $0$ . Consider the mul…

math.AG2022

Tube classes over elementary vanishing cycles

Erjuan Fu

Let $X$ be a closed Riemann surface. When $X$ is embedded into a projective space, the first rational cohomology group can be concretely obtained from the monodromy in the family o…

math.AG2022

A new approach towards Lefschetz $(1, 1)$ -Theorem

Erjuan Fu

Let $S$ be a complex projective surface. Lefschetz originally proved Lefschetz $(1, 1)$ --Theorem by studying a Lefschetz pencil of hyperplane sections of $S$ and the Abel--Jacobi m…

math.CA2021★ 1 cited

Spectrum of the Lamé operator along $Re τ = 1 / 2 :$ The genus $3$ case

Erjuan Fu

In this paper, we study the spectrum $σ (L)$ of the Lamé operator \begin{equation*}L=\frac{d^2}{dx^2}-12\wp(x+z_0;τ)\quad \text{in}\;\;L^2(\mathbb{R}, \mathbb{C}), \end{equation*} w…

math.CA2020★ 1 cited

A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $R$

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

In this paper, we study the spectrum of the complex Hill operator $L = \frac{d ^{2}}{d x ^{2}} + q (x; τ)$ in $L^{2} (R, C)$ with the Darboux-Treibich-Verdier potential \[q(x;τ):=…

Geometric analysis on rhombus torus: Green function with two singularities

Classification of spherical metrics on tori with four singularities, I: half periods

On monodromy and spectral geometry of generalized Lamé equations with four singularities, I: half periods

Green functions, Hitchin's formula and curvature equations on tori II: Rectangular torus

Green functions, Hitchin's formula and curvature equations on tori

Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations

Tube classes over elementary vanishing cycles

A new approach towards Lefschetz (1,1)-Theorem

Spectrum of the Lamé operator along Reτ=1/2: The genus 3 case

A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in R

A new approach towards Lefschetz $(1, 1)$ -Theorem

Spectrum of the Lamé operator along $Re τ = 1 / 2 :$ The genus $3$ case

A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $R$