  Nodal sets of eigenfunctions of elliptic operators on compact manifolds have
been studied extensively over the past decades. In this note, we initiate the
study of nodal sets of eigenfunctions of hypoelliptic operators on compact
manifolds, focusing on sub-Laplacians. A standard example is the sum of squares
of bracket-generating vector fields on compact quotients of the Heisenberg
group. Our results show that nodal sets behave in an anisotropic way which can
be analyzed with standard tools from sub-Riemannian geometry such as
sub-Riemannian dilations, nilpotent approximation and desingularization at
singular points. Furthermore, we provide a simple example demonstrating that
for sub-Laplacians, the Hausdorff measure of nodal sets of eigenfunctions
cannot be bounded above by $\sqrt\lambda$, which is the bound conjectured by
Yau for Laplace-Beltrami operators on smooth manifolds.
