Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The cut-off covering spectrum
HTML articles powered by AMS MathViewer

by Christina Sormani and Guofang Wei PDF
Trans. Amer. Math. Soc. 362 (2010), 2339-2391 Request permission

Abstract:

We introduce the $R$ cut-off covering spectrum and the cut-off covering spectrum of a metric space or a Riemannian manifold. The spectra measure the sizes of localized holes in the space and are defined using covering spaces called $\delta$ covers and $R$ cut-off $\delta$ covers. They are investigated using $\delta$ homotopies which are homotopies via grids whose squares are mapped into balls of radius $\delta$.

On locally compact spaces, we prove that these new spectra are subsets of the closure of the length spectrum. We prove the $R$ cut-off covering spectrum is almost continuous with respect to the pointed Gromov-Hausdorff convergence of spaces and that the cut-off covering spectrum is also relatively well behaved. This is not true of the covering spectrum defined in our earlier work, which was shown to be well behaved on compact spaces. We close by analyzing these spectra on Riemannian manifolds with lower bounds on their sectional and Ricci curvature and their limit spaces.

References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 54E45, 53C20
  • Retrieve articles in all journals with MSC (2010): 54E45, 53C20
Additional Information
  • Christina Sormani
  • Affiliation: Graduate School and University Center, CUNY, New York, New York 10016 – and – Lehman College, CUNY, Bronx, New York 10468
  • MR Author ID: 637216
  • ORCID: 0000-0002-2295-2585
  • Email: sormanic@member.ams.org
  • Guofang Wei
  • Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106
  • MR Author ID: 252129
  • Email: wei@math.ucsb.edu
  • Received by editor(s): October 31, 2007
  • Published electronically: December 3, 2009
  • Additional Notes: The first author was partially supported by a grant from the City University of New York PSC-CUNY Research Award Program
    The second author was partially supported by NSF Grant # DMS-0505733
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2339-2391
  • MSC (2010): Primary 54E45, 53C20
  • DOI: https://doi.org/10.1090/S0002-9947-09-04916-2
  • MathSciNet review: 2584603