Existence and regularity of isometries

By Michael Taylor. 2006

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We use local harmonic coordinates to establish sharp results on the regularity of isometric maps between Riemannian manifolds whose metric tensors have limited regularity (e.g., are Holder continuous). We also discuss the issue of local flatness and of local isometric embedding with given first and second fundamental form, in the context of limited smoothness.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ec81b7f5443e510e6bef5e9c7e4ee33367ab107