We consider the heat equation associated with a class of second order hypoelliptic HÃ¶rmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

%B Nonlinear Analysis %V 164 %P 118 - 134 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X17302298 %R https://doi.org/10.1016/j.na.2017.09.002