Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type

2013/03/08 by Klas Diederich, John Erik Fornæss, Diederich, Klas +5
Mathematics · #32H02 #32T15 #32T25 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32H02 #msc:32T15 #msc:32T25

paper · pdf · doi:10.48550/arxiv.1303.1976

arxiv created 2013/03/08 · openalex publication_date 2013/03/08 · arxiv updated 2013/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any bounded domain Ω⊂\Cp ⁿ of 1-type 2k which is locally convexifiable at p∈ bΩ, having a Stein neighborhood basis, there is a biholomorphic map f:Ω→ \Cp ⁿ such that f(p) is a global extreme point of type 2k for f(Ω).

Related

• Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
• Characterizing strong pseudoconvexity, obstructions to biholomorphisms,\n and Lyapunov exponents
• On defining functions for unbounded pseudoconvex domains
• An Example on s-H-Convexity in ℂ²
• Finite type domains with hyperbolic orbit accumulation points