Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911906715926528 |
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| author | Nguyen, Ngoc Cuong |
| author_facet | Nguyen, Ngoc Cuong |
| contents | We prove that the regularity of the extremal function of a compact subset of a compact Kähler manifold is a local property, and that the continuity and Hölder continuity are equivalent to classical notions of the local $L$-regularity and the locally Hölder continuous property in pluripolential theory. As a consequence we give an effective characterization of the $(\Cc^\al, \Cc^{\al'})$-regularity of compact sets, the notion introduced by Dinh, Ma and Nguyen. Using this criterion all compact fat subanalytic subsets in $\bR^n$ are shown to be regular in this sense. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_04171 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds Nguyen, Ngoc Cuong Complex Variables Differential Geometry We prove that the regularity of the extremal function of a compact subset of a compact Kähler manifold is a local property, and that the continuity and Hölder continuity are equivalent to classical notions of the local $L$-regularity and the locally Hölder continuous property in pluripolential theory. As a consequence we give an effective characterization of the $(\Cc^\al, \Cc^{\al'})$-regularity of compact sets, the notion introduced by Dinh, Ma and Nguyen. Using this criterion all compact fat subanalytic subsets in $\bR^n$ are shown to be regular in this sense. |
| title | Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2305.04171 |