拉格朗日和各向同性环面的多面体逼近

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry 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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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.