  Defect of compactness, relative to an embedding of two Banach spaces E and F,
is a difference between a weakly convergent sequence in E and its weak limit
taken up to a remainder that vanishes in the norm of F. For Sobolev embeddings
in particular, defect of compactness is expressed as a profile decomposition -
a sum of terms, called elementary concentrations, with asymptotically disjoint
supports. We discuss a profile decomposition for the Sobolev space of a
Riemannian manifold with bounded geometry, which is a sum of elementary
concentrations associated with concentration profiles defined on manifolds
different from M, that are induced by a limiting procedure. The profiles
satisfy an inequality of Plancherel type, and a similar relation, related to
the Brezis-Lieb Lemma, holds for Lebesgue norms of profiles on the respective
manifolds.
