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math.DG2026
Polynomial area growth for special Kähler metrics
Yiqian Shi, Ke Wang, Bin Xu
Let be an affine special Kähler metric on a punctured disc and let be its associated holomorphic cubic differential. We prove that if the -area of con…
math.DG2024
Solutions to Toda system with cone singularities via toric curves on compact Riemann surfaces
Jingyu Mu, Yiqian Shi, Bin Xu
On a compact Riemann surface (X) with finite punctures (P_1, \ldots, P_k), we define toric curves as multi-valued, totally unramified holomorphic maps to (\mathbb{P}^n) with monodr…
math.DG2023
The space of germs of extremal K\" ahler metrics in one dimension comprises three distinct components
Qing Chen, Yiqian Shi, Bin Xu
In the 1980s, Eugenio Calabi introduced the concept of {\it extremal K\" ahler metrics} as critical points of the -norm functional of scalar curvature in the space of K\" ahle…