5 papers
Finite Time Noncollapsing Kähler-Ricci Flow: Gaussian Type Heat Kernel, Gromov-Hausdorff Limits
Lei Zhang, Zhenlei Zhang
In this paper, we study heat kernel estimates along the Kähler-Ricci flow with finite time noncollapsing singularities over a compact Kähler manifold. The starting point is the typ…
Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes
Quang-Tuan Dang, Lei Zhang, Bin Zhou
In this paper, we establish a stability estimate and a uniform estimate for the modulus of continuity of solutions to the degenerate complex Monge-Ampère equation in big cohomology…
Uniform estimates for complex Monge-Ampère equations: big cohomology classes
Quang-Tuan Dang, Lei Zhang, Bin Zhou
We prove uniform a priori estimates for solutions to degenerate complex Monge--Ampère equations in big cohomology classes, using both auxiliary-function technique developed by Guo,…
Convergence of Scalar Curvature of Long Time Kähler-Ricci Flow on Kähler Manifold
Lei Zhang, Zhenlei Zhang
This paper is concerned with a class of the long time Kähler-Ricci flow on a compact Kähler manifold. It is shown that the uniform -entropy or uniform Sobolev inequality along t…
Complex Monge-Ampère equation in Orlicz space and Diameter Bound
Lei Zhang, Zhenlei Zhang
In this paper, we establish diameter bounds for compact Kähler manifolds equipped with Kähler metrics , assuming the associated measure lies in a specific Orlicz space and satis…