18 citations · 72 across the 32 of their papers we have counts for
35 papers
Transverse rational curves and the LeBrun--Salamon conjecture
Zhengyu Hu, Kefeng Liu, Xueyuan Wan
We prove that every compact connected positive quaternionic--Kähler manifold of real dimension with is isometric to a Wolf space after rescaling the metric by a positi…
Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
Xueyuan Wan
We prove that if a compact Kähler manifold admits a Hermitian metric with quasi-negative holomorphic sectional curvature for the Chern connection, then its canonical bundle is ampl…
Stable ample vector bundles without semipositive Kobayashi curvature
Kefeng Liu, Xueyuan Wan
We construct slope-stable ample rank-two vector bundles on every Hirzebruch surface that admit no smooth strongly pseudoconvex Finsler metric with semipositive Kobay…
Quasi-convexity of energy functions along Teichmüller geodesics
Inkang Kim, Xueyuan Wan, Genkai Zhang
Hyperbolic length functions are among the most fundamental ones on Teichmüller space, and they are quasi-convex along Teichmüller geodesics. In this paper, we investigate the same…
Positivity of the third Chern form for Griffiths positive vector bundles
Xueyuan Wan
In this paper, we prove the positivity of the double mixed discriminant associated with a positive linear map between spaces of third-order complex matrices, thereby settling the t…
Positivity of Schur forms for strongly decomposably positive vector bundles
Xueyuan Wan
In this paper, we define two types of strongly decomposable positivity, which serve as generalizations of (dual) Nakano positivity and are stronger than the decomposable positivity…
Curvature of the total space of a Griffiths negative vector bundle and quasi-Fuchsian space
Inkang Kim, Xueyuan Wan, Genkai Zhang
For a holomorphic vector bundle over a Hermitian manifold there are two important notions of curvature positivity, the Griffiths positivity and Nakano positivity. We study…
The mass of an asymptotically hyperbolic end and distance estimates
Xiaoxiang Chai, Xueyuan Wan
Let be a complete connected -dimensional Riemannian spin manifold without boundary such that the scalar curvature satisfies and …
Band width estimates of CMC initial data sets
Xiaoxiang Chai, Xueyuan Wan
We generalize a band width estimate of Gromov to CMC initial data sets. We give three independent proofs: via the stability of a hypersurface with prescribed null expansion, via a…
Signature for flat unitary bundles over surfaces with boundary
Inkang Kim, Pierre Pansu, Xueyuan Wan
This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the sign…
Signature, Toledo invariant and surface group representations in the real symplectic group
Inkang Kim, Pierre Pansu, Xueyuan Wan
In this paper, by using Atiyah-Patodi-Singer index theorem, we obtain a formula for the signature of a flat symplectic vector bundle over a surface with boundary, which is related…
Harmonic maps between surfaces homotopic to a (branched) covering map
Inkang Kim, Xueyuan Wan
In the paper, we consider the harmonic maps between surfaces and in the homotopy class of a (branched) covering map . We prove the uniqueness of critical points of ene…
Convexity of energy function associated to the harmonic maps between surfaces
Inkang Kim, Xueyuan Wan, Genkai Zhang
For a fixed smooth map between two Riemann surfaces and with non-zero degree, we consider the energy function on Teichmüller space $\mc{T}$ of that assigns to a c…
Curvature of the base manifold of a Monge-Ampère fibration and its existence
Xueyuan Wan, Xu Wang
In this paper, we consider a special relative Kähler fibration that satisfies a homogenous Monge-Ampère equation, which is called a Monge-Ampère fibration. There exist two canonica…
New Kähler metric on quasifuchsian space and its curvature properties
Inkang Kim, Xueyuan Wan, Genkai Zhang
Let be the quasifuchsian space of a closed surface of genus . We construct a new mapping class group invariant Kähler metric on . It is an extension of…
Plurisuperharmonicity of reciprocal energy function on Teichmuller space and Weil-Petersson metrics
Inkang Kim, Xueyuan Wan, Genkai Zhang
We consider harmonic maps in a fixed homotopy class from Riemann surfaces of genus varying in the Teichmü{}ller space $\mathcal…
Complex Finsler vector bundles with positive Kobayashi curvature
Huitao Feng, Kefeng Liu, Xueyuan Wan
In this short note, we prove that a complex Finsler vector bundle with positive Kobayashi curvature must be ample, which partially solves a problem of S. Kobayashi posed in 1975. A…
Plurisubharmonicity and geodesic convexity of energy function on Teichmüller space
Inkang Kim, Xueyuan Wan, Genkai Zhang
Let $π:\mc{X}\to \mc{T}$ be Teichmüller curve over Teichmüller space $\mc{T}$, such that the fiber $\mc{X}_z=π^{-1}(z)$ is exactly the Riemann surface given by the complex structur…
Remarks on the geodesic-Einstein metrics of a relative ample line bundle (with an appendix by Xu Wang)
Xueyuan Wan
In this paper, we introduce the associated geodesic-Einstein flow for a relatively ample line bundle over the total space of a holomorphic fibration and obtain a…
Logarithmic vanishing theorems for effective -ample divisors
Kefeng Liu, Xueyuan Wan, Xiaokui Yang
Let be a compact Kähler manifold and be a simple normal crossing divisor. If is the support of some effective -ample divisor, we show $$ H^q(X,Ω^p_X(\log D))=0,\quad…
A logarithmic -equation on a compact Kähler manifold associated to a smooth divisor
Xueyuan Wan
In this paper, we solve a logarithmic -equation on a compact Kähler manifold associated to a smooth divisor by using the cyclic covering trick. As applications, we…
The asymptotics of the -curvature and the second variation of analytic torsion on Teichmüller space
Xueyuan Wan, Genkai Zhang
We consider the relative canonical line bundle and a relatively ample line bundle over the total space of…
Norm estimates and asymptotic faithfulness of the quantum representations of the mapping class groups
Xueyuan Wan, Genkai Zhang
We give a direct proof for the asymptotic faithfulness of the quantum representations of the mapping class groups using peak sections in Kodaira embedding. We give also est…
Positivity preserving along a flow over projective bundle
Xueyuan Wan
In this paper, we introduce a flow over the projective bundle , which is a natural generalization of both Hermitian-Yang-Mills flow and Kähler-Ricci flow. We prove t…