2021/06/09 by Antonio Alarcón, Alarcon, Antonio
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · doi:10.48550/arxiv.2106.04950
openalex publication_date 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the open unit ball \mathbbBn of ℂn (n≥ 2) admits a nonsingular holomorphic foliation \mathcal F by closed complex hypersurfaces such that both the union of the complete leaves of \mathcal F and the union of the incomplete leaves of \mathcal F are dense subsets of \mathbbBn. In particular, every leaf of \mathcal F is both a limit of complete leaves of \mathcal F and a limit of incomplete leaves of \mathcal F. This gives the first example of a holomorphic foliation of \mathbbBn by connected closed complex hypersurfaces having a complete leaf that is a limit of incomplete ones. We obtain an analogous result for foliations by complex submanifolds of arbitrary pure codimension q with 1≤ q