Double ball property for non-divergence horizontally elliptic operators on step two Carnot groups (Q1932672)

Summary: Let \(\mathcal L\) be a linear second order horizontally elliptic operator on a Carnot group of step two. We assume \(\mathcal L\) in non-divergence form and with measurable coefficients. Then, we prove the Double Ball Property for the nonnegative sub-solutions of \(\mathcal L\). With our result, in order to solve the Harnack inequality problem for this kind of operators, it becomes sufficient to prove the so called \(\epsilon\)-Critical Density.