Invariants and heat kernels in 3D contact sub-Riemannian geometry

Davide Barilari

(SISSA, Trieste)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 10, 2011, time: 17:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. In this talk describe the two functional invariants of a 3D contact sub-Riemannian structure, discussing their role in the classification of left-invariant sub-Riemannian structures on three dimensional Lie groups.
We then 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.