Convex domains with locally Levi-flat boundaries

2011/12/08 by Николай Николов, Nikolov, Nikolai, Pascal J. Thomas +1
Mathematics · #32T27 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1112.1867

openalex publication_date 2011/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that a domain in \Cⁿ which is locally convex and has \mathcal C¹-smooth Levi-flat boundary is locally linearly equivalent to a Cartesian product of a planar domain and \C^n-1. This result does not extend to the case where the Levi form has locally constant rank for some k

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