## Mathematical and Statistical Sciences Faculty Publications and Presentations

#### Document Type

Conference Proceeding

#### Publication Date

1-2016

#### Abstract

There continues to be great interest in the study of the heat equation on Riemannian manifolds. This may be due to the remarkable more recent work of Patodi [1]. It may also be due in part to the asymptotic expansion of Minakshisundaram and Pleijel. The heat equation involves a parabolic partial differential equation that describes the distribution of heat in a given region over time. This equation has also appears in probability theory to describe random walks. The heat equation is also of importance in Riemannian geometry, topology and applied mathematics.

#### Recommended Citation

Bracken, Paul. "An Application of the Spectral Theorem To The Laplacian on a Riemannian Manifold." Proceedings of the Jangjeon Mathematical Society. Vol. 19. No. 3. 2016.

#### Publication Title

Proceedings of the Jangjeon Mathematical Society