Heat content and mean curvature

Abstract

We use distance function methods to obtain results on the heat content of a domain in an arbitrary Riemannian manifold. In particular, we give an algorithm for the calculation of the complete asymptotic series (for small times) of the heat content of a domain with smooth boundary, and the first three terms of this expansion for convex polyhedrons of arbitrary dimensions. We also write optimal upper and lower bounds of the heat content when the Ricci curvature of the domain and the mean curvature of its boundary are non-negative.

Keywords

• heat content
• distance function
• asymptotic expansions