An annulus and a half-helicoid maximize Laplace eigenvalues
Sinan Ariturk
Pontifícia Universidade Católica do Rio de Janeiro, Brazil
![An annulus and a half-helicoid maximize Laplace eigenvalues cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-8-issue-2.png&w=3840&q=90)
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