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
Abstract:
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 $z = f(x,y)$.References
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- 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
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 252-258
- MSC: Primary 53C45
- DOI: https://doi.org/10.1090/S0002-9939-1976-0420518-1
- MathSciNet review: 0420518