Richard Melrose (MIT)
Eigenvalues of collapsing triangles
Abstract:
I will describe joint work with Daniel Grieser on the behaviour
of the eigenvalues for the Dirichlet (or Neumann) problem for the standard
Laplace operator on a triangle as the triangle collapses. More precisely we
show the existence of a complete asymptotic expansion of the
eigenvalues at the boundary of a compactification of the moduli space. This
is perhaps more intricate than might at first be supposed and is a good model
problem to serve as a guide to many similar (open) questions.