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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Bernstein-type theorems in semi-Riemannian warped products
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by F. Camargo, A. Caminha and H. de Lima PDF
Proc. Amer. Math. Soc. 139 (2011), 1841-1850 Request permission

Abstract:

This paper deals with complete hypersurfaces immersed in the $(n+1)$-dimensional hyperbolic and steady state spaces. By applying a technique of S. T. Yau and imposing suitable conditions on both the $r$-th mean curvatures and on the norm of the gradient of the height function, we obtain Bernstein-type results in each of these ambient spaces.
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Additional Information
  • F. Camargo
  • Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil 58109-970
  • Email: fernandaecc@dme.ufcg.edu.br
  • A. Caminha
  • Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, Ceará, Brazil 60455-760
  • Email: antonio.caminha@gmail.com
  • H. de Lima
  • Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil 58109-970
  • MR Author ID: 800981
  • Email: henrique@dme.ufcg.edu.br
  • Received by editor(s): November 6, 2009
  • Received by editor(s) in revised form: March 29, 2010, and May 18, 2010
  • Published electronically: October 8, 2010
  • Additional Notes: The second author is partially supported by CNPq
    The third author is partially supported by PPP/FAPESQ/CNPq
  • Communicated by: Richard A. Wentworth
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1841-1850
  • MSC (2010): Primary 53C42; Secondary 53B30, 53C50, 53Z05, 83C99
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10597-X
  • MathSciNet review: 2763771