Calculus of Variations and Geometric Measure Theory

D. Barilari

Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry

created by barilari on 12 Apr 2012
modified on 12 Dec 2013


Published Paper

Inserted: 12 apr 2012
Last Updated: 12 dec 2013

Journal: Journal of Mathematical Science
Year: 2013


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.