Maximal spectral surfaces of revolution converge to a catenoid

Sinan Ariturk

doi:10.1098/rspa.2016.0239

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arXiv · 1603.08496

Maximal spectral surfaces of revolution converge to a catenoid

Sinan Ariturk

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Abstract

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 $Σ_j$ which maximizes the $j$-th 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.

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Sinan Ariturk. 2016-09-12. Maximal spectral surfaces of revolution converge to a catenoid. https://doi.org/10.1098/rspa.2016.0239

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