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.
"A Note on the Fundamental Solution of the Heat Operator on Forms." Missouri J. Math. Sci. 25 (2) 186 - 194, November 2013. https://doi.org/10.35834/mjms/1384266203