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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Relative isometric embeddings of Riemannian manifolds


Authors: Mohammad Ghomi and Robert E. Greene
Journal: Trans. Amer. Math. Soc. 363 (2011), 63-73
MSC (2010): Primary 53C42, 53A07
Published electronically: August 16, 2010
MathSciNet review: 2719671
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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.


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Additional Information

Mohammad Ghomi
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: ghomi@math.gatech.edu

Robert E. Greene
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
Email: greene@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05095-0
PII: S 0002-9947(2010)05095-0
Keywords: Relative isometric embedding, Riemannian manifold, short map
Received by editor(s): April 28, 2008
Published electronically: August 16, 2010
Additional Notes: The first-named author was supported by NSF Grant DMS-0336455 and CAREER award DMS-0332333.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.