The spectrum of a compact Riemannian manifold is one of the most important analytic invariants in Riemannian geometry. In particular, the first (non-trivial) eigenvalue of the Laplacian of a compact space subvariety is one of its intrinsic first order invariants. The study of this invariant and its relation to other extrinsic invariants is a central research topic not only from a geometrical point of view, but also within relevant mathematical aspects of General Relativity.