Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909015825448960 |
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| author | Ahn, Hyunsoo |
| author_facet | Ahn, Hyunsoo |
| contents | For a compact subset in a compact Hermitian manifold, we prove that the continuity of the extremal function at a given point in the set is a local property and that the continuity of a weighted extremal function follows from the continuities of the extremal function and the weight function. These results are generalizations of the results of Nguyen \cite{Ng24} on compact Kähler manifolds. Moreover, for a compact subset in a compact Hermitian manifold, at the point level and accordingly at the global level, we characterize the continuity of the extremal function via the local \(L\)-regularity, which is equivalent to the weak local \(L\)-regularity. We also show that the \(L\)-regularity of a compact subset in \(\mathbb{C}^n\) at a star center implies the local \(L\)-regularity. Consequently, a convex compact \(L\)-regular subset in \(\mathbb{C}^n\) is locally \(L\)-regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01885 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds Ahn, Hyunsoo Complex Variables For a compact subset in a compact Hermitian manifold, we prove that the continuity of the extremal function at a given point in the set is a local property and that the continuity of a weighted extremal function follows from the continuities of the extremal function and the weight function. These results are generalizations of the results of Nguyen \cite{Ng24} on compact Kähler manifolds. Moreover, for a compact subset in a compact Hermitian manifold, at the point level and accordingly at the global level, we characterize the continuity of the extremal function via the local \(L\)-regularity, which is equivalent to the weak local \(L\)-regularity. We also show that the \(L\)-regularity of a compact subset in \(\mathbb{C}^n\) at a star center implies the local \(L\)-regularity. Consequently, a convex compact \(L\)-regular subset in \(\mathbb{C}^n\) is locally \(L\)-regular. |
| title | Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2604.01885 |