Degenerate complex Hessian equations with arbitrary measure in bounded domains
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914208653770752 |
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| author | Van Phu, Nguyen Hai, Le Mau |
| author_facet | Van Phu, Nguyen Hai, Le Mau |
| contents | Let $Ω$ be a bounded strictly $m$-pseudoconvex domain of $\mathbb{C}^n$. We solve degenerate complex Hessian equations of the form $(ω+ dd^c φ)^m\wedgeβ^{n-m} = μ$ in the generalized Cegrell classes $\mathcal{K}_m(Ω,ω,ϕ)$, where $ϕ\in \mathcal{E}_m(Ω)$ is a $m$-maximal function, $ω$ is a smooth real $(1,1)$-form defined in a neighborhood of $\barΩ$ and $μ$ is a positive Radon measure which is dominated by a Hessian measure of $m$-subharnomic functions in Cegrell class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerate complex Hessian equations with arbitrary measure in bounded domains Van Phu, Nguyen Hai, Le Mau Complex Variables 32U05, 32Q15, 32W20 Let $Ω$ be a bounded strictly $m$-pseudoconvex domain of $\mathbb{C}^n$. We solve degenerate complex Hessian equations of the form $(ω+ dd^c φ)^m\wedgeβ^{n-m} = μ$ in the generalized Cegrell classes $\mathcal{K}_m(Ω,ω,ϕ)$, where $ϕ\in \mathcal{E}_m(Ω)$ is a $m$-maximal function, $ω$ is a smooth real $(1,1)$-form defined in a neighborhood of $\barΩ$ and $μ$ is a positive Radon measure which is dominated by a Hessian measure of $m$-subharnomic functions in Cegrell class. |
| title | Degenerate complex Hessian equations with arbitrary measure in bounded domains |
| topic | Complex Variables 32U05, 32Q15, 32W20 |
| url | https://arxiv.org/abs/2504.08592 |