Heat content of a Riemannian manifold with a perfect conducting boundary (Q1811021)

Let \(M\) be a compact smooth Riemannian manifold with smooth boundary. It is established existence of an asymptotics series for the heat content of \(M\) with a perfect conducting boundary. It is shown that the coefficients in the series are non-local invariants which are recursively determined by the coefficients for the series with corresponding zero Dirichlet boundary condition.