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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On A. Hurwitz’ method in isoperimetric inequalities


Author: Isaac Chavel
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
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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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Keywords: Sectional curvatures, minimal submanifold, volume, area, eigenvalues of Laplacian
Article copyright: © Copyright 1978 American Mathematical Society