Riemann surfaces and totally real tori

  • Julien Duval

    Université Paris-Sud, Orsay, France
  • Damien Gayet

    Université Joseph Fourier Grenoble 1, Saint-Martin-d'Hères, France


Given a totally real torus unknotted in the unit sphere S3S^3 of C2\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.

Cite this article

Julien Duval, Damien Gayet, Riemann surfaces and totally real tori. Comment. Math. Helv. 89 (2014), no. 2, pp. 299–312

DOI 10.4171/CMH/320