2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172605We 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.34 pagesAnalysis of PDEsProbability35K05 (Primary); 74Q10 (Secondary)text