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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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Discrete connection Laplacians
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by Svetoslav Zahariev PDF
Proc. Amer. Math. Soc. 136 (2008), 3717-3726 Request permission

Abstract:

To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial, metric dependent Laplacians associated to triangulations of $M$ and prove that their spectra converge, as the mesh of the triangulations approaches zero, to the spectrum of the connection Laplacian.
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Additional Information
  • Svetoslav Zahariev
  • Affiliation: Department of Mathematics and Computer Science, Lehman College of CUNY, 250 Bedford Park Boulevard West, Bronx, New York 10468
  • Email: szahariev@gc.cuny.edu
  • Received by editor(s): July 17, 2007
  • Received by editor(s) in revised form: September 13, 2007
  • Published electronically: May 19, 2008
  • Communicated by: Mikhail Shubin
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3717-3726
  • MSC (2000): Primary 58J50
  • DOI: https://doi.org/10.1090/S0002-9939-08-09359-3
  • MathSciNet review: 2415060