# Heat Flow Out of a Compact Manifold

@article{Berg2013HeatFO,
title={Heat Flow Out of a Compact Manifold},
author={Michiel van den Berg and Peter Gilkey},
journal={The Journal of Geometric Analysis},
year={2013},
volume={25},
pages={1576-1601}
}
• Published 26 June 2013
• Mathematics
• The Journal of Geometric Analysis
We discuss the heat content asymptotics associated with the heat flow out of a smooth compact manifold in a larger compact Riemannian manifold. Although there are no boundary conditions, the corresponding heat content asymptotics involve terms localized on the boundary. The classical pseudo-differential calculus is used to establish the existence of the complete asymptotic series, and methods of invariance theory are used to determine the first few terms in the asymptotic series in terms of…
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