Inserted: 12 apr 2012
Last Updated: 12 dec 2013
Journal: Journal of Mathematical Science
In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in terms of the two basic functional invariants χ and κ defined on a 3D contact structure.