7 citations · 10 across the 14 of their papers we have counts for
16 papers
Reduced Solutions of Toda Systems for Arbitrary Complex Simple Lie Algebras
Yiqian Shi, Chunhui Wei, Bin Xu
We study reduced solutions of Toda systems generated by spherical metrics for an arbitrary complex simple Lie algebra. The main result is an intrinsic centralizer parametrization:…
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…
Zariski-Dense Monodromy of Singular Hyperbolic Metrics on Non-Hyperbolic Riemann Surfaces
Yu Feng, Yiqian Shi, Jijian Song +1
We prove that the monodromy group of every singular hyperbolic metric on a non-hyperbolic Riemann surface, in the sense of potential theory, is Zariski dense in ${\rm PSL}(2,\mathb…
The Hurwitz existence problem and the prime-degree conjecture: A computational perspective
Yiru Wang, Bingqian Li, Yi Zhou +4
We investigate the Hurwitz existence problem from a computational viewpoint. Leveraging the symmetric-group algorithm by Zheng and building upon implementations originally develope…
Solution to SU(n+1) Toda system generated by spherical metrics
Yiqian Shi, Chunhui Wei, Bin Xu
Using the correspondence between solutions to the SU(n+1) Toda system on a Riemann surface and totally unramified unitary curves, we show that a spherical metric generates a fa…
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…
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…
Classifying solutions of Toda system around a singular source
Jingyu Mu, Yiqian Shi, Tianyang Sun +1
Consider a positive integer and . Let , and let denote the Cartan matrix of . Utilizing…
Solutions of the Toda system from meromorphic functions
Yiqian Shi, Chunhui Wei, Bin Xu
We consider the Toda system on a simply connected domain in , the case of which coincides with the Liouville equation . A classical r…
Singular hyperbolic metrics and negative subharmonic functions
Yu Feng, Yiqian Shi, Jijian Song +1
We propose a conjecture that the monodromy group of a singular hyperbolic metric on a non-hyperbolic Riemann surface is {\it Zariski dense} in . By using m…
Characterizing isolated singularities of conformal hyperbolic metrics
Yu Feng, Yiqian Shi, Bin Xu
We find the explicit local models of isolated singularities of conformal hyperbolic metrics by Complex Analysis, which is interesting in its own and could potentially be extended t…
Isolated singularities of conformal hyperbolic metrics
Yu Feng, Yiqian Shi, Bin Xu
J. Nitsche proved that an isolated singularity of a conformal hyperbolic metric is either a conical singularity or a cusp one. We prove by developing map that there exists a comple…
Gradient estimate of a Neumann eigenfunction on a compact manifold with boundary
Jingchen Hu, Yiqian Shi, Bin Xu
Let be a Neumann eigenfunction with respect to the positive Laplacian on a compact Riemannian manifold with boundary such that in the interior of…
Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
Yiqian Shi, Bin Xu
Let be an eigenfunction with respect to the Dirichlet Laplacian on a compact Riemannian manifold with boundary: in the interior of and $e_ł…
Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary
Yiqian Shi, Bin Xu
Let be an eigenfunction with respect to the Laplace-Beltrami operator on a compact Riemannian manifold without boundary: . We show the following…
The Riemannian manifolds with boundary and large symmetry
Zhi Chen, Yiqian Shi, Bin Xu
Sixty years ago, S. B. Myers and N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a struct…