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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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Nonlinear waves on 3D hyperbolic space
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by Jason Metcalfe and Michael Taylor PDF
Trans. Amer. Math. Soc. 363 (2011), 3489-3529 Request permission

Abstract:

In this article, global-in-time dispersive estimates and Strichartz estimates are explored for the wave equation on three dimensional hyperbolic space. Due to the negative curvature, extra dispersion is noted, as compared to the Euclidean case, and a wider range of Strichartz estimates is proved. Using these, small data global existence to semilinear wave equations is shown for a range of powers that is broader than that known for Euclidean space.
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Additional Information
  • Jason Metcalfe
  • Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
  • MR Author ID: 733199
  • Email: metcalfe@email.unc.edu
  • Michael Taylor
  • Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
  • MR Author ID: 210423
  • Email: met@email.unc.edu
  • Received by editor(s): March 26, 2009
  • Published electronically: February 24, 2011
  • Additional Notes: The second author was partially supported by NSF grants DMS-0800678 and DMS-0758320
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3489-3529
  • MSC (2000): Primary 35L70
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05122-6
  • MathSciNet review: 2775816