Weighted energy class of $m$-subharmonic functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929358692679680 |
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| author | Anh, H. T. Phu, N. V. Dieu, N. Q. |
| author_facet | Anh, H. T. Phu, N. V. Dieu, N. Q. |
| contents | In this paper, we introduce the class $\mathcal{E}_{m,F}(Ω)$ and solve complex $m$-Hessian equations in the class $\mathcal{E}_{m,F}(Ω)$. Afterthat, we study subextension in the class $\mathcal{E}_{m,F}(Ω)$ with the weighted Hessian measure of subextension unchanged. This is an extensive version of the result in [24] in the case when the smaller domain is relatively compact inside the large one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08904 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted energy class of $m$-subharmonic functions Anh, H. T. Phu, N. V. Dieu, N. Q. Complex Variables 32U05, 32W20 In this paper, we introduce the class $\mathcal{E}_{m,F}(Ω)$ and solve complex $m$-Hessian equations in the class $\mathcal{E}_{m,F}(Ω)$. Afterthat, we study subextension in the class $\mathcal{E}_{m,F}(Ω)$ with the weighted Hessian measure of subextension unchanged. This is an extensive version of the result in [24] in the case when the smaller domain is relatively compact inside the large one. |
| title | Weighted energy class of $m$-subharmonic functions |
| topic | Complex Variables 32U05, 32W20 |
| url | https://arxiv.org/abs/2307.08904 |