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" Jöricke `onion' structure. We illustrate these phenomena with explicit examples of parabolic knots and links with mixed components.
From: Ali Elgindi [view email]
[v1]
Tue, 23 Jun 2026 08:06:32 UTC (6 KB)
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