6 papers
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,…
Hölder Regularity of Dirichlet Problem For The Complex Monge-Ampère Equation
Yuxuan Hu, Bin Zhou
We study the Dirichlet problem for the complex Monge-Ampère equation on a strictly pseudoconvex domain in Cn or a Hermitian manifold. Under the condition that the right-hand side l…
A topological rigidity theorem on noncompact Hessian manifolds
Hanzhang Yin, Bin Zhou
In this work, we obtain a short time solution for a geometric flow on noncompact affine Riemannian manifolds. Using this result, we can construct a Hessian metric with nonnegative…
Sobolev inequalities and regularity of the linearized complex Monge-Ampere and Hessian equations
Jiaxiang Wang, Bin Zhou
Let be a smooth, strictly -plurisubharmonic function on a bounded domain with . The purpose of this paper is to study the regularity of solu…
Trace Inequalities, isocapacitary inequalities and regularity of the complex Hessian equations
Jiaxiang Wang, Bin Zhou
In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger type), isocapacitary inequalities and the regularity of the complex Hessian and Monge-A…