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arXiv · 2502.03357

Rationally Convex Surfaces with hyperbolic complex tangencies

Georgios Dimitroglou Rizell·Mark G. Lawrence
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Abstract

We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by handle-bodies, and those that do not have any compact Riemann surfaces attached at all. The fillable examples all live in the round sphere and are unknotted, while the non-fillable examples can moreover be produced in several different smooth isotopy classes.

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BibTeXRIS

Georgios Dimitroglou Rizell, Mark G. Lawrence. 2025-02-05. Rationally Convex Surfaces with hyperbolic complex tangencies. https://arxiv.org/abs/2502.03357

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