## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 25, Issue 2 (2013), 186-194.

### A Note on the Fundamental Solution of the Heat Operator on Forms

#### Abstract

An approximate solution of the heat equation on $p$-forms on an $n$-dimensional manifold is constructed. This is used to create a fundamental solution of the heat operator. It is shown there is a link between this solution and the generalized Gauss-Bonnet Theorem on manifolds.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 25, Issue 2 (2013), 186-194.

**Dates**

First available in Project Euclid: 12 November 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1384266203

**Digital Object Identifier**

doi:10.35834/mjms/1384266203

**Mathematical Reviews number (MathSciNet)**

MR3059315

**Zentralblatt MATH identifier**

1281.58017

**Subjects**

Primary: 58A12: de Rham theory [See also 14Fxx]

Secondary: 58I35 53C99: None of the above, but in this section

**Keywords**

heat operator $p$-form manifold Laplacian

#### Citation

Bracken, Paul. A Note on the Fundamental Solution of the Heat Operator on Forms. Missouri J. Math. Sci. 25 (2013), no. 2, 186--194. doi:10.35834/mjms/1384266203. https://projecteuclid.org/euclid.mjms/1384266203