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- W3022761640 abstract "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." @default.
- W3022761640 created "2020-05-13" @default.
- W3022761640 creator A5018396117 @default.
- W3022761640 date "2020-05-03" @default.
- W3022761640 modified "2023-09-26" @default.
- W3022761640 title "Isometric immersions of RCD spaces" @default.
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- W3022761640 doi "https://doi.org/10.48550/arxiv.2005.01222" @default.
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