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Existence and regularity of isometries
Author:
Michael Taylor
Journal:
Trans. Amer. Math. Soc. 358 (2006), 2415-2423
MSC (2000):
Primary 35J15, 53A07, 53C21
Posted:
January 24, 2006
MathSciNet review:
2204038
Full-text PDF Free Access
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Additional Information
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.
References
- [AKLT]
M. Anderson, A. Katsuda, Y. Kurylev, M. Lassas, and M. Taylor, Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem, Invent. Math. 158 (2004), 261-321. MR 2096795 (2005h:53051)
- [CH]
E. Calabi and P. Hartman, On the smoothness of isometries, Duke Math. J. 37 (1970), 741-750. MR 0283727 (44:957)
- [CL]
P. Ciarlet and F. Larsonneur, On the recovery of a surface with prescribed first and second fundamental form, J. Math. Pure Appl. 81 (2002), 167-185. MR 1994608 (2004e:53001)
- [DTK]
D. DeTurk and J. Kazdan, Some regularity theorems in Riemannian geometry, Ann. Scient. Ecole Norm. Sup. Paris 14 (1981), 249-260. MR 0644518 (83f:53018)
- [H]
P. Hartman, On the local uniqueness of geodesics, Amer. J. Math. 72 (1950), 723-730. MR 0038111 (12:357b)
- [HW1]
P. Hartman and A. Wintner, On the fundamental equations of differential geometry, Amer. J. Math. 72 (1950), 757-774. MR 0038110 (12:357a)
- [HW2]
P. Hartman and A. Wintner, On the existence of Riemannian manifolds which cannot carry non-constant analytic or harmonic functions in the small, Amer. J. Math. 75 (1953), 260-276. MR 0055016 (14:1015g)
- [HW3]
P. Hartman and A. Wintner, On uniform Dini conditions in the theory of linear partial differential equations of elliptic type, Amer. J. Math. 77 (1955), 329-353. MR 0074669 (17:627c)
- [LY]
A. Lytchak and A. Yaman, On Hölder continuous Riemannian and Finsler metrics, Preprint, 2004.
- [MS]
S. Meyers and N. Steenrod, The group of isometries of a Riemannian manifold, Ann. of Math. 40 (1939), 400-416. MR 1503467
- [P]
C. Pugh, The
 conclusion in Gromov's theory, Ergod. Theory Dynam. Sys. 7 (1987), 133-147. MR 0886375 (88d:53039)
- [T1]
M. Taylor, Partial Differential Equations, Vols. 1-3, Springer-Verlag, New York, 1996. MR 1395147 (98b:35002a)
- [T2]
M. Taylor, Tools for PDE, Math. Surv. and Monogr. #81, AMS, Providence, R.I., 2000. MR 1766415 (2001g:35004)
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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
Posted:
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 after
28 years from publication.
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