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

 

Existence and regularity of isometries


Author: Michael Taylor
Journal: Trans. Amer. Math. Soc. 358 (2006), 2415-2423
MSC (2000): Primary 35J15, 53A07, 53C21
Published electronically: January 24, 2006
MathSciNet review: 2204038
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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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Additional Information

Michael Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: met@math.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04090-6
PII: S 0002-9947(06)04090-6
Received by editor(s): April 7, 2004
Published electronically: January 24, 2006
Additional Notes: This work was partially supported by NSF grant DMS-0139726
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.