3 papers
math.DG2025
Approximating sub-riemannian structures by Riemannian metrics and spectral convergence
Leo Harakeh, Luc Hillairet
We construct an approximating sequence of Riemannian metrics tailored to a given sub-Riemannian structure. We prove that the sequence of associated Riemannian volumes converge to P…
math-ph2025
Cauchy Data for 1D singular Schrödinger operators
Luc Hillairet, Jeremy L. Marzuola
We study semiclassical 1-D Schrödinger operators of the form on a finite interval for . We show…
math.SP2024
Generic simplicity of ellipses
Luc Hillairet, Chris M. Judge
We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the…