An annulus and a half-helicoid maximize Laplace eigenvalues

  • Sinan Ariturk

    Pontifícia Universidade Católica do Rio de Janeiro, Brazil

Abstract

The Dirichlet eigenvalues of the Laplace–Beltrami operator are larger on an annulus than on any other surface of revolution in with the same boundary. This is established by defining a sequence of shrinking cylinders about the axis of symmetry and proving that flattening a surface outside of each cylinder successively increases the eigenvalues. A similar argument shows that the Dirichlet eigenvalues of the Laplace–Beltrami operator are larger on a half-helicoid than on any other screw surface in with the same boundary.

Cite this article

Sinan Ariturk, An annulus and a half-helicoid maximize Laplace eigenvalues. J. Spectr. Theory 8 (2018), no. 2, pp. 315–346

DOI 10.4171/JST/198