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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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Nonrigidity of a class of two dimensional surfaces with positive curvature and planar points
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by A. Meziani PDF
Proc. Amer. Math. Soc. 141 (2013), 2137-2143 Request permission

Abstract:

Existence of nontrivial infinitesimal bendings is established for an orientable surface with boundary $S\subset \mathbb {R}^3$ that has positive curvature except at finitely many planar points and such that $H_1(S)=0$. As an application, we show that any neighborhood of such a surface $S$ (for the $C^k$ topology) contains isometric surfaces that are noncongruent.
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Additional Information
  • A. Meziani
  • Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
  • MR Author ID: 239413
  • Email: meziani@fiu.edu
  • Received by editor(s): December 10, 2009
  • Received by editor(s) in revised form: October 4, 2011
  • Published electronically: January 25, 2013
  • Communicated by: Sergei K. Suslov
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2137-2143
  • MSC (2010): Primary 53A05; Secondary 30G20, 35F05
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11488-7
  • MathSciNet review: 3034439