18 citations · 67 across the 17 of their papers we have counts for
17 papers
Two families of reducible spherical conical metrics
Haoran Wu, Xuwen Zhu
We analyze a 1-parameter family of heart shape and a 3-parameter family obtained by gluing three footballs, both of which are examples of reducible spherical conical metrics. For t…
Tian--Yau metrics: Fredholm theory, Hodge cohomology and moduli spaces
Rafe Mazzeo, Xuwen Zhu
We study the natural geometric elliptic operators on a class of complete Riemannian manifolds which include the 4-dimensional ALH* gravitational instantons and their higher dimensi…
A gluing construction of ALF gravitational instantons and existence of non-holomorphic minimal spheres
Xuwen Zhu
This note extends the construction of ALF gravitational instantons in Schroers--Singer to a new case where the nonlinear superposition is given by the Atiyah--Hitch…
Degenerating hyperbolic surfaces and spectral gaps for large genus
Yunhui Wu, Haohao Zhang, Xuwen Zhu
In this article we study the differences of two consecutive eigenvalues up to for the Laplacian on hyperbolic surfaces of genus , and show that the supr…
Learning trends of COVID-19 using semi-supervised clustering
Semhar Michael, Xuwen Zhu, Volodymyr Melnykov
A finite mixture model is used to learn trends from the currently available data on coronavirus (COVID-19). Data on the number of confirmed COVID-19 related cases and deaths for Eu…
Spherical conical metrics and harmonic maps to spheres
Mikhail Karpukhin, Xuwen Zhu
A spherical conical metric on a surface is a metric of constant curvature with finitely many isolated conical singularities. The uniformization problem for such metrics…
Skewed Distributions or Transformations? Modelling Skewness for a Cluster Analysis
Michael P. B. Gallaugher, Paul D. McNicholas, Volodymyr Melnykov +1
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the G…
Fundamental gaps of spherical triangles
Shoo Seto, Guofang Wei, Xuwen Zhu
We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical lunes and the spherical triangles which are half the lunes, and show that the fundamental gap goes to i…
Spectral properties of reducible conical metrics
Bin Xu, Xuwen Zhu
We show that the monodromy of a spherical conical metric is reducible if and only if it has a real-valued eigenfunction with eigenvalue 2 in the holomorphic extension of the associ…
Conical metrics on Riemann surfaces, II: spherical metrics
Rafe Mazzeo, Xuwen Zhu
We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier p…
Rigidity of a family of spherical conical metrics
Xuwen Zhu
We study the deformation of spherical conical metrics with at least some of the cone angles larger than . We show in this note via synthetic geometry that for one family of suc…
Spherical conic metrics and realizability of branched covers
Xuwen Zhu
Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constr…
Conical metrics on Riemann surfaces, I: the compactified configuration space and regularity
Rafe Mazzeo, Xuwen Zhu
We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above thi…
Boundary behaviour of Weil-Petersson and fiber metrics for Riemann moduli spaces
Richard Melrose, Xuwen Zhu
The Weil-Petersson and Takhtajan-Zograf metrics on the Riemann moduli spaces of complex structures for an -fold punctured oriented surface of genus in the stable range $g+2…
The eleven dimensional supergravity equations on edge manifolds
Xuwen Zhu
We study the eleven dimensional supergravity equations which describe a low energy approximation to string theories and are related to M-theory under the AdS/CFT correspondence. Th…
Eigenvalue resolution of self-adjoint matrices
Xuwen Zhu
Resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown tha…
Resolution of the canonical fiber metrics for a Lefschetz fibration
Richard Melrose, Xuwen Zhu
We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by sho…