## 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