Parabolic equations on uniformly regular Riemannian manifolds and   degenerate initial boundary value problems
  In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying approach to problems with strong degeneracies in the interior or at the boundary. 
Herbert Amann
math.DG math.AP