论文标题
RCD空间的等距浸入
Isometric immersions of RCD spaces
论文作者
论文摘要
我们证明，如果RCD空间在欧几里得空间中有常规的等距浸入，那么浸入浸入是局部的Bi-Lipschitz嵌入图。该结果导致我们证明，如果紧凑的非汇总RCD空间通过特征模型在欧几里得空间中具有等轴测浸入，那么eigenmap是将bi-lipschitz嵌入到球体中的本地bi-lipschitz，将takeorem theorem of theorem of theorem theorem submanifold Themotion submanifold Themits置于非smmomt otmorts设置。这些结果的应用包括一个拓扑球定理和拓扑定理，即使对于封闭的Riemannian歧管，它们都是新的。
We prove that if an RCD space has a regular isometric immersion in a Euclidean space, then the immersion is a locally bi-Lipschitz embedding map. This result leads us to prove that if a compact non-collapsed RCD space has an isometric immersion in a Euclidean space via an eigenmap, then the eigenmap is a locally bi-Lipschitz embedding map to a sphere, which generalizes a fundamental theorem of Takahashi in submanifold theory to a non-smooth setting. Applications of these results include a topological sphere theorem and topological finiteness theorems, which are new even for closed Riemannian manifolds.
