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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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On A. Hurwitz’ method in isoperimetric inequalities
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by Isaac Chavel PDF
Proc. Amer. Math. Soc. 71 (1978), 275-279 Request permission

Abstract:

We show that if M is complete simply connected with nonpositive sectional curvatures, $\Omega$ a minimal submanifold of M with connected suitably oriented boundary $\Gamma$ then ${\lambda ^{1/2}}V/A \leqslant {(n - 1)^{1/2}}/n$ where V is the volume of $\Omega$, A the volume of $\Gamma ,\lambda$ the first nonzero eigenvalue of the Laplacian of $\Gamma$, and $n( \geqslant 2)$ is the dimension of $\Omega$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 275-279
  • MSC: Primary 53C40
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0493885-2
  • MathSciNet review: 0493885