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.

VL - 164 UR - http://www.sciencedirect.com/science/article/pii/S0362546X17302298 ER -