14 citations · 95 across the 20 of their papers we have counts for
22 papers
Global estimate for complex Monge--Ampère equations on compact Kähler manifolds
Haozhao Li, Bing Wang, Kai Zheng
In this paper, we prove a global estimate for the complex Monge--Ampère equation with a positive right-hand side on a compact Kähler manifold.
Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants
Haozhao Li, Bing Wang, Kai Zheng
We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence o…
On the structure of complete -solitons
Haozhao Li, Yuanqing Ma, Kai Zheng
In this work, we establish compactness and regularity results for complete gradient Laplacian solitons of closed -structures. Under a lower scalar-curvature bound and a distan…
Hermitian Calabi functional in complexified orbits
Jie He, Kai Zheng
Let be a compact symplectic manifold. We denote by $\ac$ the space of all almost complex structure compatible with . $\ac$ has a natural foliation structure with the com…
The Space of Closed -Structures. I. Connections
Pengfei Xu, Kai Zheng
In this article, we develop foundational theory for geometries of the space of closed -structures in a given cohomology class as an infinite-dimensional manifold. We introduce…
Singular scalar curvature equations
Kai Zheng
We develop estimates for the equation of scalar curvature of singular metrics with cone angle , in a big and semi-positive cohomology class on a Kähler manifold. We further de…
On uniform log -stability for constant scalar curvature Kähler cone metrics
Takahiro Aoi, Yoshinori Hashimoto, Kai Zheng
We prove that the existence of constant scalar curvature Kähler metrics with cone singularities along a divisor implies log -polystability and -uniform log -stability, whe…
Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors
Long Li, Jian Wang, Kai Zheng
The purpose of this paper is to prove the a priori estimates for constant scalar curvature Kaehler metrics with conic singularities along normal crossing divisors. The zero order…
Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stability
Kai Zheng
We show that the existence of constant scalar curvature Kähler (cscK) metrics with cone singularities is equivalent to the properness of log -energy. We also prove their equival…
Geodesics in the space of Kahler cone metrics, II. Uniqueness of constant scalar curvature Kahler cone metrics
Kai Zheng
This is a continuation of the previous articles on Kahler cone metrics. In this article, we introduce weighted function spaces and provide a self-contained treatment on cone angles…
Construction of constant scalar curvature Kähler cone metrics
Julien Keller, Kai Zheng
Over a compact Kähler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a Kähler metric with conic singularities along a divisor. We de…
Expansion formula for complex Monge-Ampère equation along cone singularities
Hao Yin, Kai Zheng
In this paper, we prove the asymptotic expansion of the solutions to some singular complex Monge-Ampère equation which arise naturally in the study of the conical Kähler-Einstein m…
Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity
Long Li, Kai Zheng
The aim of this paper is to investigate uniqueness of conic constant scalar curvature Kaehler (cscK) metrics, when the cone angle is less than . We introduce a new Hölder space…
Generalized Matsushima's theorem and Kähler-Einstein cone metrics
Long Li, Kai Zheng
In this paper, we prove Matsushima's theorem for Kähler-Einstein metrics on a Fano manifold with cone singularities along a smooth divisor that is not necessarily proportional to t…
Regularity scales and convergence of the Calabi flow
Haozhao Li, Bing Wang, Kai Zheng
We define regularity scales to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal Kah…
-properness of Mabuchi's -energy
Kai Zheng
Over the space of Kähler metrics associated to a fixed Kähler class, we first prove the lower bound of the energy functional , then we provide the criterions of the geo…
On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics
Simone Calamai, David Petrecca, Kai Zheng
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the com…
Kähler non-collapsing, eigenvalues and the Calabi flow
Haozhao Li, Kai Zheng
We first proved a compactness theorem of the Kähler metrics, which confirms a prediction of Chen. Then we prove several eigenvalue estimates along the Calabi flow. Combining the co…
The Dirichlet and the weighted metrics for the space of Kahler metrics
Simone Calamai, Kai Zheng
In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we c…
Stability of Calabi flow near an extremal metric
Hongnian Huang, Kai Zheng
We prove that on a Kähler manifold admitting an extremal metric and for any Kähler potential close to , the Calabi flow starting at exists for all time and the m…
Stability of Kähler-Ricci flow in the space of Kähler metrics
Kai Zheng
In this paper, we prove that on a Fano manifold which admits a Kähler-Ricci soliton $(\om,X)$, if the initial Kähler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense…
Pseudo-Calabi Flow
Xiuxiong Chen, Kai Zheng
We first define Pseudo-Calabi flow, as {equation*} {{aligned}{{\partial φ}\over {\partial t}}&= -f(φ), \triangle_varphi f(φ) &= S(φ) - \ul S.{aligned}. \end{equation*} Then we prov…