Holomorphic functions unbounded on curves of finite length

2014/12/09 by Josip Globevnik, Globevnik, Josip
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1412.2916

16 pages

arxiv created 2014/12/09 · openalex publication_date 2014/12/09 · arxiv updated 2014/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A consequence is the existence of a complete closed complex hypersurface M in D such that the lengths of paths p:[0,1]--> M, with p(0) fixed, grow arbitrarily fast as p(1)-->bD.

Citations

• Complete bounded embedded complex curves in C²

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