$C^k$-quasi-isometry sets are pre-compact
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- by F. T. Farrell and P. Ontaneda PDF
- Proc. Amer. Math. Soc. 138 (2010), 737-741 Request permission
Abstract:
Let $M$ be a closed smooth manifold. By an argument formally similar to one used in constructing the Levi-Civita connection, it is shown that $C^k$-quasi-isometry sets in $DIFF^{k+1}(M)$ are $C^{k+1}$-bounded, where $0\leq k< \infty$. This implies, using the Arsela-Ascoli theorem, that such sets are pre-compact in $DIFF^{k}(M)$.References
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Additional Information
- F. T. Farrell
- Affiliation: Department of Mathematics, State University of New York, Binghamton, New York 13902
- MR Author ID: 65305
- P. Ontaneda
- Affiliation: Department of Mathematics, State University of New York, Binghamton, New York 13902
- MR Author ID: 352125
- Received by editor(s): March 4, 2009
- Received by editor(s) in revised form: March 6, 2009
- Published electronically: October 9, 2009
- Additional Notes: Both authors were partially supported by NSF grants.
- Communicated by: Chuu-Lian Terng
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 737-741
- MSC (2000): Primary 58A05, 58D05, 58D17, 58D19
- DOI: https://doi.org/10.1090/S0002-9939-09-10132-6
- MathSciNet review: 2557190