18 citations · 72 across the 32 of their papers we have counts for
23 papers · 1 filter
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 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…
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…
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…
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…
The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle
Xueyuan Wan, Genkai Zhang
Let be a holomorphic fibration with compact fibers and a relatively ample line bundle over . We obtain the asymptotic of the curvature of $L^2…
Compact Kähler manifolds with positive orthogonal bisectional curvature
Huitao Feng, Kefeng Liu, Xueyuan Wan
In this short note, using Siu-Yau's method [14], we give a new proof that any n-dimensional compact Kahler manifold with positive orthogonal bisectional curvature must be biholomo…
Holomorphic sectional curvature of complex Finsler manifolds
Xueyuan Wan
In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian man…
Geodesic-Einstein metrics and nonlinear stabilities
Huitao Feng, Kefeng Liu, Xueyuan Wan
In this paper, we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic-Einstein metric on th…
A Donaldson type functional on a holomorphic Finsler vector bundle
Huitao Feng, Kefeng Liu, Xueyuan Wan
In this paper, we solve a problem of Kobayashi posed in \cite{Ko4} by introducing a Donaldson type functional on the space of strongly pseudo-convex complex Finsler metric…
Chern forms of holomorphic Finsler vector bundles and some applications
Huitao Feng, Kefeng Liu, Xueyuan Wan
In this paper, we present two kinds of total Chern forms and as well as a total Segre form of a holomorphic Finsler vector bundle $π:(E,G)\to M…
Rational curves on Hermitian manifolds
Huitao Feng, Kefeng Liu, Xueyuan Wan +1
By using analytic method, we prove that there exist rational curves on compact Hermitian manifolds with positive holomorphic bisectional curvature. It confirms a question of S.-T.…