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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Two remarks on the length spectrum of a Riemannian manifold
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by Benjamin Schmidt and Craig J. Sutton PDF
Proc. Amer. Math. Soc. 139 (2011), 4113-4119 Request permission

Abstract:

We demonstrate that every closed manifold of dimension at least two admits smooth metrics with respect to which the length spectrum is not a discrete subset of the real line. In contrast, we show that the length spectrum of any real analytic metric on a closed manifold is a discrete subset of the real line. In particular, the length spectrum of any closed locally homogeneous space forms a discrete set.
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Additional Information
  • Benjamin Schmidt
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 803074
  • Email: schmidt@math.msu.edu
  • Craig J. Sutton
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
  • MR Author ID: 707441
  • ORCID: 0000-0003-2197-1407
  • Email: craig.j.sutton@dartmouth.edu
  • Received by editor(s): June 23, 2010
  • Received by editor(s) in revised form: September 27, 2010
  • Published electronically: March 25, 2011
  • Additional Notes: The first author’s research was partially supported by NSF grant DMS-0905906.
    The second author’s research was partially supported by NSF grant DMS-0605247 and a Career Enhancement Fellowship from the Woodrow Wilson National Fellowship Foundation
  • Communicated by: Jianguo Cao
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 4113-4119
  • MSC (2010): Primary 53C22
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10815-3
  • MathSciNet review: 2823056