An Application of the Spectral Theorem To The Laplacian on a Riemannian Manifold

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

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