拉格朗日和各向同性环面的多面体逼近

Pub Date : 2020-12-10 DOI:10.4310/jsg.2022.v20.n6.a4

Yann Rollin

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引用次数: 1

摘要

我们证明了$\mathbb{R}^4$的每一个光滑浸没的2-环面都可以用浸没的多面体拉格朗日环面在c0意义上近似。在平稳浸没的情况下。嵌入的)拉格朗日环面$\mathbb{R}^4$时，表面可以通过浸入(R}^4$)在c1意义上近似。嵌入的)多面体拉格朗日环面。对于$\mathbb{R}^{2n}$的各向同性2-环面也证明了类似的命题。

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Polyhedral approximation by Lagrangian and isotropic tori

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 $\mathbb{R}^{2n}$.

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