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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.

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Eigenvalue and gap estimates for the Laplacian acting on $p$-forms
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by Pierre Guerini and Alessandro Savo PDF
Trans. Amer. Math. Soc. 356 (2004), 319-344 Request permission

Abstract:

We study the gap of the first eigenvalue of the Hodge Laplacian acting on $p$-differential forms of a manifold with boundary, for consecutive values of the degree $p$. We first show that the gap may assume any sign. Then we give sufficient conditions on the intrinsic and extrinsic geometry to control it. Finally, we estimate the first Hodge eigenvalue of manifolds whose boundaries have some degree of convexity.
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Additional Information
  • Pierre Guerini
  • Affiliation: Institut für Mathematik, Universität Zürich Irchel, Winterthurerstrasse 90, CH-8057 Zürich, Switzerland
  • Email: pguerini@math.unizh.ch
  • Alessandro Savo
  • Affiliation: Dipartimento di Metodi e Modelli Matematici, Università di Roma I La Sapienza, Via Antonio Scarpa 16, 00161 Roma, Italy
  • Email: savo@dmmm.uniroma1.it
  • Received by editor(s): January 13, 2003
  • Published electronically: August 25, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 319-344
  • MSC (2000): Primary 58J50; Secondary 58J32
  • DOI: https://doi.org/10.1090/S0002-9947-03-03336-1
  • MathSciNet review: 2020035