Relative isometric embeddings of Riemannian manifolds

Mohammad Ghomi; Robert E. Greene

doi:10.1090/s0002-9947-2010-05095-0

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Relative isometric embeddings of Riemannian manifolds

Mohammad Ghomi Robert E. Greene

Year: 2010 Journal: Transactions of the American Mathematical Society Vol: 363 (01)Pages: 63-63 Publisher: American Mathematical Society

DOI: 10.1090/s0002-9947-2010-05095-0

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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.

Keywords:

Mathematics Isometric exercise Pure mathematics Euclidean space Point (geometry) Euclidean geometry Mathematical analysis Geometry

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Geometric Analysis and Curvature Flows

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Numerical methods in inverse problems

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Point processes and geometric inequalities

Physical Sciences → Mathematics → Applied Mathematics

Relative isometric embeddings of Riemannian manifolds

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