  In this paper, we define a new capacity which allows us to control the
behaviour of the Dirichlet spectrum of a compact Riemannian manifold with
boundary, with "small" subsets (which may intersect the boundary) removed. This
result generalizes a classical result of Rauch and Taylor ("the crushed ice
theorem"). In the second part, we show that the Dirichlet spectrum of a
sequence of bounded Euclidean domains converges to the spectrum of a ball with
the same volume, if the first eigenvalue of these domains converges to the
first eigenvalue of a ball.
