Polyhedral approximation by Lagrangian and isotropic tori

Abstract

We prove that every smoothly immersed 2-torus of ${\mathbb{R}}^4$ can be approximated, in the C0-sense, by immersed polyhedral Lagrangian tori. In the case of a smoothly immersed (resp. embedded) Lagrangian torus of ${\mathbb{R}}^4$, the surface can be approximated in the C1-sense by immersed (resp. embedded) polyhedral Lagrangian tori. Similar statements are proved for isotropic 2-tori of ${\mathbb{R}}^{2n}$.

25 pages, 3 figures, minor changes for v4, some references added, to appear in Journal of Symplectic Geometry