3 papers
math.AP2008
Eigenfunction concentration for polygonal billiards
Andrew Hassell, Luc Hillairet, Jeremy Marzuola
In this note, we extend the results on eigenfunction concentration in billiards as proved by the third author in \cite{M1}. There, the methods developed in Burq-Zworski \cite{BZ3}…
math.SP2008
The eigenvalues of the Laplacian on domains with small slits
Luc Hillairet, Chris Judge
We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to…
math.SP2007
Generic spectral simplicity of polygons
Luc Hillairet, Chris Judge
We study the Laplace operator with Dirichlet or Neumann boundary condition on polygons in the Euclidean plane. We prove that almost every simply connected polygon with at least fou…