Given a totally real torus unknotted in the unit sphere of , 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.
Cite this article
Julien Duval, Damien Gayet, Riemann surfaces and totally real tori. Comment. Math. Helv. 89 (2014), no. 2, pp. 299–312DOI 10.4171/CMH/320