Geometry Seminar
Spectral simplicity of the curl operator on generic smoothly bounded domains
Speaker: Josef Greilhuber (Stanford)Date: Wednesday, 26 March 2025 - 15:00Place: Aula Naranja, ICMAT
Abstract:
We consider the curl operator acting on boundary-parallel, divergence free vector fields on a three-dimensional smoothly bounded domain. Upon imposing a finite number of additional boundary conditions, this operator becomes self-adjoint with compact resolvent, so its spectrum consists of discrete eigenvalues of finite multiplicity. We will derive a formula for the variation of these eigenvalues under domain deformations and apply it to show that for a generic smoothly bounded domain all eigenvalues are simple.
