43 citations · 74 across the 21 of their papers we have counts for
13 papers · 1 filter
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…
DtN isospectrality, flat metrics with non-trivial holonomy and comparison formula for determinants of Laplacian
Luc Hillairet, Alexey Kokotov
We study comparison formulas for -regularized determinants of self-adjoint extensions of the Laplacian on flat conical surfaces of genus . The cases of trivial and non-…
Quantum ergodicity and quantum limits for sub-Riemannian Laplacians
Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat
This paper is a proceedings version of \cite{CHT-I}, in which we state a Quantum Ergodicity (QE) theorem on a 3D contact manifold, and in which we establish some properties of the…
Spectral asymptotics for sub-Riemannian Laplacians. I: quantum ergodicity and quantum limits in the 3D contact case
Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat
This is the first paper of a series in which we plan to study spectral asymptotics for sub-Riemannian Laplacians and to extend results that are classical in the Riemannian case con…
Moduli spaces of meromorphic functions and determinant of Laplacian
Luc Hillairet, Victor Kalvin, Alexey Kokotov
The Hurwitz space is the moduli space of pairs where is a compact Riemann surface and is a meromorphic function on . We study the Laplace operator o…
Hyperbolic triangles without embedded eigenvalues
Luc Hillairet, Chris Judge
We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigen…