Heat content asymptotics of Riemannian manifolds

          by M. van den Berg, S. Desjardins and P. Gilkey,


Mathematics subject classification: 58G25, 35K05

Key words and phrases: Heat content, asymptotic formulae

Abstract: Let $M$ be a compact Riemannian manifold with smooth boundary and
let $D$ be an operator of Laplace type on $M$ with Dirichlet or modified
Neumann boundary conditions. The heat content asymptotics give the short time
heat energy content of $M$ with suitable initial conditions; we give locally
computable formulas for these invariants.