Existence and regularity of isometries

Taylor, Michael

doi:10.1090/S0002-9947-06-04090-6

Existence and regularity of isometries
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Trans. Amer. Math. Soc. 358 (2006), 2415-2423 Request permission

Abstract:

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 Hölder 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.

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