A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients

We consider weak solutions of second-order partial differential equations of Kolmogorov-Fokker-Planck-type with measurable coefficients in the form ∂tu + (v,∇xu) = div(A(v,x,t)∇vu) + (b(v,x,t),∇vu) + f, (v,x,t) ϵ2n+1, where A is a symmetric uniformly positive definite matrix with bounded measurable coefficients; f and the components of the vector b are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.