We consider the heat equation with Dirichlet boundary conditions on the
tubular neighborhood of a closed Riemannian submanifold. We show that, as the
tube radius decreases, the semigroup of a suitably rescaled and renormalized
generator can be effectively described by a Hamiltonian on the submanifold with
a potential that depends on the geometry of the submanifold and of the
embedding.Comment: 34 page