Holomorphic Hulls for Compact 3-Manifolds

Ali M. Elgindi

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arXiv · 2606.24951

Holomorphic Hulls for Compact 3-Manifolds

Ali M. Elgindi

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Abstract

We demonstrate the different possible structures for holomorphic hulls for embeddings of compact real 3-manifolds $M \hookrightarrow \mathbb{C}^3$ along the set of complex tangents $\gamma$. Using our previous work [1], we can construct embeddings with any prescribed link and 2-plane field along it, as well as a prescription of angles at each point that determines the Bishop invariant. We show that elliptic points ($\gamma < \frac{1}{2}$) produce analytic discs filling a Levi-flat hypersurface, hyperbolic points ($\gamma > \frac{1}{2}$) add no local hull structure, and parabolic points ($\gamma = \frac{1}{2}$) may develop a "delicate" J\"oricke `onion' structure. We illustrate these phenomena with explicit examples of parabolic knots and links with mixed components.

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Ali M. Elgindi. 2026-06-23. Holomorphic Hulls for Compact 3-Manifolds. https://arxiv.org/abs/2606.24951

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