An Example on s-H-Convexity in ℂ²

2018/07/26 by Lars Simon, Simon, Lars, Berit Stensønes +1
Mathematics · #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.1807.10185

15 pages

arxiv created 2018/07/26 · openalex publication_date 2018/07/26 · arxiv updated 2018/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a bounded domain Ω in ℂ² with boundary of class C^1,1, such that Ω has a Stein neighborhood basis, but is not s-H-convex for any real number s≥1.

Related

• An inequality characterizing convex domains
• Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type
• Good Stein Neighborhood Bases and Regularity of the d-bar Neumann Problem
• On a Problem of Bremermann Concerning Runge Domains
• Convexity of the Bergman Kernels on Convex Domains