A P ] 2 8 O ct 2 00 8 L 2-Homogenization of Heat Equations on Tubular Neighborhoods

We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian sub-manifold of a Riemannian manifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormal-ized generator can be effectively described by a Hamiltonian on the submanifold with a potential that depends… CONTINUE READING