6 papers · 1 filter
On the extension of Kähler currents on compact complex manifolds
Jiafu Ning, Kai Pang, Haoyuan Sun +2
Let be a compact Kähler manifold and let be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every -plurisubharmonic function o…
Capacity Stability of Complex Monge-Ampère Equations with Moving Prescribed Singularities
Kai Pang, Haoyuan Sun, Zhiwei Wang +1
For complex Monge-Ampère equations with moving big cohomology classes and prescribed model singularities of positive Monge-Ampère mass, we prove that, under total variation converg…
Frobenius type positivity of Hodge bundles and applications
Hao Max Sun
We define two new Frobenius type positivity notions, -ampleness and -ampleness, for coherent sheaves, show that they are stronger than ordinary ampleness and establish…
The Cauchy-Dirichlet Problem for Complex Hessian Flows: From A Priori Estimates to Pluripotential Theory
Haoyuan Sun
We study the Cauchy--Dirichlet problem for parabolic complex Hessian equations on Hermitian manifolds and on bounded strictly m-pseudoconvex domains. In the smooth setting, we prov…
Convergence of the Chern-Ricci flow on complex minimal surfaces of general type
Haoyuan Sun
We prove uniform diameter estimates, volume non-collapsing estimates and Gromov-Hausdorff convergence for the normalized Chern-Ricci flow on smooth complex minimal surfaces of gene…
Gromov-Hausdorff limits of the Chern-Ricci flow on smooth Hermitian minimal models of general type
Haoyuan Sun
We establish uniform diameter estimates and volume non-collapsing estimates for the Chern-Ricci flow on smooth Hermitian minimal models of general type, assuming the initial metric…