论文标题
通过热内核的共形嵌入
Conformal Embeddings via Heat Kernel
论文作者
论文摘要
对于任何n维紧凑型riemannian歧管$ m $，带有光滑度量$ g $，通过使用Bérard-Besson-Gallot'94引入的热内核嵌入，我们本质上构建了一个规范的结构式嵌入$ c_ {t，k} $： $ t> 0 $足够小，$ q（t）\ gg t^{ - \ frac {n} {2}}} $和$ k $作为$ O（t^l）$的函数。我们的方法涉及找到所有这些规范的保形嵌入，这表明了与Wang-Zhu'15引入的等距嵌入的区别。
For any n-dimensional compact Riemannian Manifold $M$ with smooth metric $g$, by employing the heat kernel embedding introduced by Bérard-Besson-Gallot'94, we intrinsically construct a canonical family of conformal embeddings $C_{t,k}$: $M\rightarrow\mathbb{R}^{q(t)}$, with $t>0$ sufficiently small, $q(t)\gg t^{-\frac{n}{2}}$, and $k$ as a function of $O(t^l)$ in proper sense. Our approach involves finding all these canonical conformal embeddings, which shows the distinctions from the isometric embeddings introduced by Wang-Zhu'15.
