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Spectrum of manifolds with holes. (English) Zbl 0847.58076
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.

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