Maximal spectral surfaces of revolution converge to a catenoid
Maximal spectral surfaces of revolution converge to a catenoid
We consider a maximization problem for eigenvalues of the Laplace-Beltrami operator on surfaces of revolution in $\mathbb{R}^3$ with two prescribed boundary components. For every $j$, we show that there is a surface $\Sigma_j$ which maximizes the $j$-th Dirichlet eigenvalue. The maximizing surface has a meridian which is a rectifiable curve. …