2021/07/05 by Małgorzata Stawiska, Stawiska, Małgorzata
Mathematics · #31A15 #31C15 #31D05 #32U35 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Number Theory (math.NT) #Primary 32P05 #Secondary 12J25 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2107.03539
openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define an analog of the Leja-Siciak-Zaharjuta subharmonic extremal function for a proper subset E of the Berkovich projective line P1 over a field with a non-archimedean absolute value, relative to a point ζ\not ∈ E. When E is a compact set with positive capacity, we prove that the upper semicontinuous regularization of this extremal function equals the Green function of E relative to ζ. As a separate result, we prove the Brelot-Cartan principle, under the additional assumption that the Berkovich topology is second countable.