Spectrum of manifolds with holes. (English) Zbl 0847.58076

Courtois, Gilles

J. Funct. Anal. 134, No. 1, 194-221 (1995).

The author studies the spectrum of a bounded Euclidean domain \(X\) with a compact subset of small capacity removed. In particular he shows that there is a perturbation theory for the Dirichlet spectrum of \(X \setminus A\) where \(A\) is any “small” compact subset of \(X\) and the “parameter” of the perturbation is the capacity of \(A\) itself.

Reviewer: Th.M.Rassias (Athens)

MSC:

58J50	Spectral problems; spectral geometry; scattering theory on manifolds
58J37	Perturbations of PDEs on manifolds; asymptotics
31C15	Potentials and capacities on other spaces

Keywords:

spectrum of manifolds; Euclidean domains; Dirichlet conditions; Riemannian manifold; Green function; capacity