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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An elementary proof of a finite rigidity problem by infinitesimal rigidity methods
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by Edgar Kann PDF
Proc. Amer. Math. Soc. 60 (1976), 252-258 Request permission


Let two compact, isometric surfaces with boundary be given having positive gauss curvature. If the surfaces can be placed so that their normal spherical images lie in a compact subset of a hemisphere of the unit sphere and so that the isometry is the identity on the boundary then the isometry is the identity mapping. The proof is elementary in the sense that no integral formulae or maximum principles for elliptic operators are needed. An example is given of a surface satisfying the above hypotheses which is neither convex nor has a representation in the form $z = f(x,y)$.
    S. E. Cohn-Vossen, Verbiegbarkeit von Flächen im Grossen, Fortschritte Math. 1 (1936), 33-76.
  • N. W. Efimow, Flächenverbiegung im Grossen, Akademie-Verlag, Berlin, 1957 (German). MR 0105722
  • Edgar Kann, A new method for infinitesimal rigidity of surfaces with $K>0$, J. Differential Geometry 4 (1970), 5–12. MR 259817
  • Detlef Laugwitz, Differential and Riemannian geometry, Academic Press, New York-London, 1965. Translated by Fritz Steinhardt. MR 0172184
  • A. V. Pogorelov, Extrinsic geometry of convex surfaces, Translations of Mathematical Monographs, Vol. 35, American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by Israel Program for Scientific Translations. MR 0346714
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 252-258
  • MSC: Primary 53C45
  • DOI:
  • MathSciNet review: 0420518