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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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Eigenvalue estimate on complete noncompact Riemannian manifolds and applications
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by Manfredo P. do Carmo and Detang Zhou PDF
Trans. Amer. Math. Soc. 351 (1999), 1391-1401 Request permission


We obtain some sharp estimates on the first eigenvalues of complete noncompact Riemannian manifolds under assumptions of volume growth. Using these estimates we study hypersurfaces with constant mean curvature and give some estimates on the mean curvatures.
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Additional Information
  • Manfredo P. do Carmo
  • Affiliation: IMPA, Estrada Dona Castorina, 110-Jardim Botanico 22460-320 Rio de Janeiro, Brazil
  • Email: manfredo@
  • Detang Zhou
  • Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong 250100, China
  • Received by editor(s): November 15, 1996
  • Received by editor(s) in revised form: February 28, 1997
  • Additional Notes: Supported partially by NNSFC and TWAS-IMPA membership
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1391-1401
  • MSC (1991): Primary 53C42; Secondary 53A10, 53C20, 35J60
  • DOI:
  • MathSciNet review: 1451597