Relative isometric embeddings of Riemannian manifolds

Ghomi, Mohammad; Greene, Robert

doi:10.1090/S0002-9947-2010-05095-0

Relative isometric embeddings of Riemannian manifolds
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by Mohammad Ghomi and Robert E. Greene PDF

Trans. Amer. Math. Soc. 363 (2011), 63-73 Request permission

Abstract:

We prove the existence of $C^1$ isometric embeddings, and $C^\infty$ approximate isometric embeddings, of Riemannian manifolds into Euclidean space with prescribed values in a neighborhood of a point.

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