Mixed Hessian inequalities on Hermitian manifolds and applications

Haoyuan Sun

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arXiv · 2512.08552

Mixed Hessian inequalities on Hermitian manifolds and applications

Haoyuan Sun

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Abstract

Let $(X,\omega)$ be a compact Hermitian manifold of complex dimension $n$. In this paper we establish a Ko\l odziej-Nguyen type weak convergence theorem of complex Hessian operators. Utilizing this result, we prove a general mixed Hessian inequality with respect to a background Hermitian metric, covering both local and global case. As an application, we prove the existence of bounded solutions of complex Hessian equations where the right-hand side measure is well dominated by capacities.

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Haoyuan Sun. 2025-12-09. Mixed Hessian inequalities on Hermitian manifolds and applications. https://arxiv.org/abs/2512.08552

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