Complete bounded embedded complex curves in C²

2013/05/09 by Antonio Alarcón, Antonio Alarcon, Francisco J. López +3 · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1305.2118

To appear in J. Eur. Math. Soc. (JEMS)

openalex publication_date 2013/05/09 · arxiv created 2016/06/07 · arxiv updated 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any convex domain of C² carries properly embedded complete complex curves. In particular, we exhibit the first examples of complete bounded embedded complex curves in C²

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• Holomorphic functions unbounded on curves of finite length

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