Continuity of solutions to complex Hessian equations on compact Hermitian manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915558489849856 |
|---|---|
| author | Fang, Yuetong |
| author_facet | Fang, Yuetong |
| contents | Let $(X,ω)$ be a compact Hermitian manifold of dimension $n$. We derive an $L^\infty$-estimate for bounded solutions to the complex $m$-th Hessian equations on $X$, assuming a positive right-hand side in the Orlicz space $L^{\frac{n}{m}}(\log L)^n(h\circ\log \circ \log L)^n$, where the associated weight satisfies Kołodziej's Condition. Building upon this estimate, we then establish the existence of continuous solutions to the complex Hessian equation under the prescribed assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuity of solutions to complex Hessian equations on compact Hermitian manifolds Fang, Yuetong Complex Variables Differential Geometry 32W20, 32U05, 32Q15, 35A23 Let $(X,ω)$ be a compact Hermitian manifold of dimension $n$. We derive an $L^\infty$-estimate for bounded solutions to the complex $m$-th Hessian equations on $X$, assuming a positive right-hand side in the Orlicz space $L^{\frac{n}{m}}(\log L)^n(h\circ\log \circ \log L)^n$, where the associated weight satisfies Kołodziej's Condition. Building upon this estimate, we then establish the existence of continuous solutions to the complex Hessian equation under the prescribed assumptions. |
| title | Continuity of solutions to complex Hessian equations on compact Hermitian manifolds |
| topic | Complex Variables Differential Geometry 32W20, 32U05, 32Q15, 35A23 |
| url | https://arxiv.org/abs/2510.14690 |