18 citations · 72 across the 32 of their papers we have counts for
7 papers · 1 filter
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 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…
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…
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…
Geometry of logarithmic forms and deformations of complex structures
Kefeng Liu, Sheng Rao, Xueyuan Wan
We present a new method to solve certain -equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The resul…
Logarithmic vanishing theorems on compact Kähler manifolds I
Chunle Huang, Kefeng Liu, Xueyuan Wan +1
In this paper, we first establish an -type Dolbeault isomorphism for logarithmic differential forms by Hörmander's -estimates. By using this isomorphism and the construct…