论文标题
一个半决赛程序，将扁平托里的变形嵌入到希尔伯特空间中
A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces
论文作者
论文摘要
我们得出并分析了一个无限维半菲尼斯程序，该程序计算Flat Tori $ \ Mathbb {R}^n/L $的最小失真嵌入，其中$ l $是$ n $ diperimential lattice，in Hilbert Space。这使我们能够比以前最佳的下界不断改善因素，以最小的嵌入$ n $维平面圆环的变形。随着进一步的应用，我们证明，每个$ n $维二维的扁平圆环具有有限的尺寸最小的失真嵌入，标准游览的标准嵌入是最佳的，我们确定所有$ 2 $ dimensional flat flat tori的最小失真嵌入。
We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori $\mathbb{R}^n/L$, where $L$ is an $n$-dimensional lattice, into Hilbert spaces. This enables us to provide a constant factor improvement over the previously best lower bound on the minimal distortion of an embedding of an $n$-dimensional flat torus. As further applications we prove that every $n$-dimensional flat torus has a finite dimensional least distortion embedding, that the standard embedding of the standard tours is optimal, and we determine least distortion embeddings of all $2$-dimensional flat tori.
