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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On an integral formula for closed hypersurfaces of the sphere
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by Chorng-shi Houh
Proc. Amer. Math. Soc. 35 (1972), 234-237
DOI: https://doi.org/10.1090/S0002-9939-1972-0296867-3

Abstract:

In a compact oriented hypersurface ${M^n}$ of the sphere ${S^{n + 1}}$ the integral formula ${\smallint _{{M^n}}}\nabla {K_r}dV = n{\smallint _{{M^n}}}({K_r}{K_1} - {K_{r + 1}})edV$ is proved where ${K_r}$ is the rth mean curvature, e is the unit normal of ${M^n}$ in ${S^{n + 1}}$. Some applications are considered.
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 234-237
  • MSC: Primary 53C45
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0296867-3
  • MathSciNet review: 0296867