HEAT-CONTENT ASYMPTOTICS OF A RIEMANNIAN MANIFOLD WITH BOUNDARY

Let M be a compact Riemannian manifold with a smooth C(infinity) boundary partial derivative M. Suppose M has initial temperature 1 at time t = 0 and suppose that partial derivative M is kept at temperature 0 for all t > 0. We study the asymptotic behavior of the amount of heat in M as t --> 0+. We generalize these results to arbitrary operators of Laplace type with Dirichlet boundary conditions and to arbitrary smooth initial conditions. (C) 1994 Academic Press, Inc.