7 papers
A realizability criterion for rational maps with three branch points
Zhiqiang Wei
Let \[ π_{0}=[\underbrace{2,\ldots,2}_{2s-1}],\quad π_{\infty}=[\underbrace{3,\ldots,3}_{s},\underbrace{1,\ldots,1}_{s-2}],\quad π_{1}=[γ_{1},γ_{2},γ_{3}] \] be three nontrivial pa…
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…
A note on Rational Maps with three branching points on the Riemann sphere
Zhiqiang Wei, Yingyi Wu, Bin Xu
Studying the existence of rational functions with given branching datum is a classical problem in the field of complex analysis and algebraic geometry. This problem dates back to H…
Geometric structure and existence of reducible spherical conical metrics
Zhiqiang Wei, Yingyi Wu, Bin Xu
A conformal metric with finitely many conical singularities of constant Gaussian curvature on a compact Riemann surface is referred to as a spherical conical m…
Realization of HCMU metrics in 3-dimensional space forms as Weingarten surfaces
Zhiqiang Wei, Yingyi Wu
In \cite{WeiWu22-3} (J.Geom.Anal.32, 199(2022)), we classified HCMU surfaces in 3-dimensional Euclidean space as Weingarten surfaces by holomorphic functions. In this paper, using…
Constructing constant curvature metrics on Riemann surfaces with singularities
Zhiqiang Wei
By constructing an ODE through a kind of meromorphic 1-forms, we will give an explicit construction of a kind of conformal metrics of constant curvature on Riemann surfaces with si…
On isometric minimal immersion of a singular non-CSC extremal Khler metric into 3-dimensional space forms
Zhiqiang Wei, Yingyi Wu
On any compact Riemann surface there always exists a singular non-CSC (constant scalar curvature) extremal Khler metric which is called a non-CSC HCMU (the Hessian of the…