Commentarii Mathematici Helvetici

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Volume 89, Issue 2, 2014, pp. 299–312
DOI: 10.4171/CMH/320

Published online: 2014-06-18

Riemann surfaces and totally real tori

Julien Duval[1] and Damien Gayet[2]

(1) Université Paris-Sud, Orsay, France
(2) Université Joseph Fourier Grenoble 1, Saint-Martin-d'Hères, France

Given a totally real torus unknotted in the unit sphere $S^3$ of $\mathbb{C}^2$, we prove the following alternative: either the torus is rationally convex and there exists a filling of the torus by holomorphic discs, or its rational hull contains a holomorphic annulus or a pair of holomorphic discs.

Keywords: Totally real torus, filling by holomorphic discs, rational convexity

Duval Julien, Gayet Damien: Riemann surfaces and totally real tori. Comment. Math. Helv. 89 (2014), 299-312. doi: 10.4171/CMH/320