Mixed Hessian inequalities on Hermitian manifolds and applications
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912755635716096 |
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| author | Sun, Haoyuan |
| author_facet | Sun, Haoyuan |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed Hessian inequalities on Hermitian manifolds and applications Sun, Haoyuan Differential Geometry 32W20, 32U05, 32U40, 53C55 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. 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. |
| title | Mixed Hessian inequalities on Hermitian manifolds and applications |
| topic | Differential Geometry 32W20, 32U05, 32U40, 53C55 |
| url | https://arxiv.org/abs/2512.08552 |