Spectral Theory of Operators on Manifolds

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Book

Publication Date

1-18-2017

Abstract

Differential operators that are defined on a differentiable manifold can be used to study various properties of manifolds. The spectrum and eigenfunctions play a very significant role in this process. The objective of this chapter is to develop the heat equation method and to describe how it can be used to prove the Hodge Theorem. The Minakshisundaram-Pleijel parametrix and asymptotic expansion are then derived. The heat equation asymptotics can be used to give a development of the Gauss-Bonnet theorem for two-dimensional manifolds.

Comments

© 2017 The Author(s). Licensee IntechOpen.

Recommended Citation

Paul Bracken (January 18th 2017). Spectral Theory of Operators on Manifolds, Manifolds - Current Research Areas, Paul Bracken, IntechOpen, DOI: 10.5772/67095. Available from: https://www.intechopen.com/chapters/53712

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

Publication Title

Manifolds - Current Research Areas

DOI

10.5772/67095