Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds

2023/05/07 by Ngoc Cuong Nguyen, Nguyen, Ngoc Cuong · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2305.04171

openalex publication_date 2023/05/07 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28

Abstract

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 \bRⁿ are shown to be regular in this sense.

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