ABSTRACT
In this chapter, the authors briefly summarize some of the results on the heat content asymptotics. As for the heat equation asymptotics, the results provided are valid on compact smooth Riemannian manifolds with smooth boundary. In contrast to the heat equation asymptotics, the heat content asymptotics is not known for oblique, spectral and transmittal boundary conditions and the authors restrict themselves mainly to Dirichlet and Robin boundary conditions. The authors define the heat content asymptotics as opposed to the heat equation asymptotics and present heat content calculations on the generalized cone. The heat content calculations on the generalized cone provide possibilities by which the influence of conical singularities in curved manifolds might be studied.
