Haoyuan Sun

activity

20242026

collaborators

10 papers

math.CV2026

On the extension of Kähler currents on compact complex manifolds

Jiafu Ning, Kai Pang, Haoyuan Sun +2

Let $(X, ω)$ be a compact Kähler manifold and let $V \subset X$ be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every $ω ∣_{V}$ -plurisubharmonic function o…

math.CV2026

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…

math.AG2026

Frobenius type positivity of Hodge bundles and applications

Hao Max Sun

We define two new Frobenius type positivity notions, $F^{t}$ -ampleness and $F^{t} GG$ -ampleness, for coherent sheaves, show that they are stronger than ordinary ampleness and establish…

math.AP2026

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…

math.DG2026

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…

math.DG2026

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…

math.DG2025

Mixed Hessian inequalities on Hermitian manifolds and applications

Haoyuan Sun

Let $(X, ω)$ be a compact Hermitian manifold of complex dimension $n$ . In this paper we establish a Kołodziej-Nguyen type weak convergence theorem of complex Hessian operators. Util…

math.CV2025

Degenerate Complex Hessian type equations on compact Hermitian manifolds and Applications

Kai Pang, Haoyuan Sun, Zhiwei Wang +1

The aim of this paper is to further develop the theory of the degenerate complex Hessian equations on compact Hermitian manifolds. Building upon the generalization of the Bedford-T…

math.CV2025

Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications II

Haoyuan Sun, Zhiwei Wang

Let $(X, ω)$ be a compact Hermitian manifold of complex dimension $n$ , equipped with a Hermitian metric $ω$ . Let $β$ be a possibly non-closed smooth $(1, 1)$ -form on $X$ such that $\…

math.CV2024

Weak convergence of complex Monge-Ampère operators on compact Hermitian manifolds

Kai Pang, Haoyuan Sun, Zhiwei Wang

Let $(X, ω)$ be a compact Hermitian manifold and let ${β} \in H^{1, 1} (X, R)$ be a real $(1, 1)$ -class with a smooth representative $β$ , such that $\int_{X} β^{n} > 0$ . Assume that t…