# 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} }

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…

## 23 Citations

Heat Content Asymptotics on a Compact Riemannian Manifold with Boundary

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We review the heat content asymptotics on a compact Riemannian manifold with boundary and with specific heat and initial temperature distributions. Some computation of first a few terms in the…

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In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for Lévy processes of bounded variation in Rd…

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We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing…

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