We consider a maximization problem for eigenvalues of the Laplace–Beltrami operator on surfaces of revolution in with two prescribed boundary components. For every j, we show there is a surface Σj that maximizes the jth Dirichlet eigenvalue. The maximizing surface has a meridian which is a rectifiable curve. If there is a catenoid which is the unique area minimizing surface with the prescribed boundary, then the eigenvalue maximizing surfaces of revolution converge to this catenoid.
- Received April 1, 2016.
- Accepted September 6, 2016.
- © 2016 The Author(s)
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