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Contents Online
Journal of Symplectic Geometry
Volume 20 (2022)
Number 6
Polyhedral approximation by Lagrangian and isotropic tori
Pages: 1349 – 1383
DOI: https://dx.doi.org/10.4310/JSG.2022.v20.n6.a4
Author
Abstract
We prove that every smoothly immersed $2$-torus of $\mathbb{R}^4$ can be approximated, in the $C^0$-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 $C^1$-sense by immersed (resp. embedded) polyhedral Lagrangian tori. Similar statements are proved for isotropic $2$-tori of $\mathbb{R}^{2n}$.
Published 26 April 2023