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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$C^k$-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 $DIFF^{k}(M)$.
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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