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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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Area estimates and rigidity of non-compact $H$-surfaces in 3-manifolds
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by Vanderson Lima PDF
Proc. Amer. Math. Soc. 147 (2019), 4499-4512 Request permission

Abstract:

For appropriate values of $H$, we obtain an area estimate for a complete non-compact $H$-surface of finite topology and finite area, embedded in a 3-manifold of negative curvature. Moreover, in the case of equality and under additional assumptions, we prove that a neighborhood of the mean convex side of the surface must be isometric to a hyperbolic Fuchsian manifold. Also, we provide a counterexample showing that, in the case of minimal surfaces, equality in the area estimate does not necessarily imply a local rigidity result for the ambient manifold.
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Additional Information
  • Vanderson Lima
  • Affiliation: Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Porto Alegre - RS 90040-060 Brazil
  • MR Author ID: 1200287
  • ORCID: 0000-0003-3740-2348
  • Email: vanderson.lima@ufrgs.br
  • Received by editor(s): May 15, 2018
  • Received by editor(s) in revised form: February 1, 2019
  • Published electronically: May 17, 2019
  • Additional Notes: This work started while the author was working at Instituto Nacional de Matemática Pura e Aplicada (IMPA) under the fund Programa de Capacitação Institucional PCI/MCTI-CNPq.
  • Communicated by: Jiaping Wang
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4499-4512
  • MSC (2010): Primary 53A10, 53Axx
  • DOI: https://doi.org/10.1090/proc/14578
  • MathSciNet review: 4002559