Complete embedded complex curves in the ball of \(\mathbb{C}^2\) can have any topology

DOI10.2140/apde.2017.10.1987zbMath1384.32014arXiv1611.06913OpenAlexW2963689985MaRDI QIDQ2402624

Josip Globevnik, Antonio Alarcón

Publication date: 12 September 2017

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.06913

zbMATH Keywords

complex curvesholomorphic embeddingscomplete bounded submanifolds

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Embedding of analytic spaces (32C22) Analytic subsets of affine space (32B15)

Related Items (11)

The first thirty years of Andersén-Lempert theory ⋮ Complete complex hypersurfaces in the ball come in foliations ⋮ Wild holomorphic foliations of the ball ⋮ Complex curves in pseudoconvex Runge domains containing discrete subsets ⋮ Foliations on the open 3-ball by complete surfaces ⋮ Complete nonsingular holomorphic foliations on Stein manifolds ⋮ A foliation of the ball by complete holomorphic discs ⋮ Construction of labyrinths in pseudoconvex domains ⋮ The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends ⋮ Holomorphic Legendrian curves in \(\mathbb{CP}^3\) and superminimal surfaces in \(\mathbb{S}^4\) ⋮ Complete densely embedded complex lines in ℂ²

Cites Work

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• Holomorphic functions unbounded on curves of finite length
• Complete proper holomorphic embeddings of strictly pseudoconvex domains into balls
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• Subalgebras of functions on a Riemann surface
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• Curvatures of complex submanifolds of \(C^n\)
• Null curves in \({\mathbb{C}^3}\) and Calabi-Yau conjectures
• Stein Manifolds and Holomorphic Mappings
• Complete bounded holomorphic curves immersed in $\mathbb {C}^2$ with arbitrary genus
• A Complete Bounded Complex Submanifold of C 3

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