Horizontal mean curvature flow and nonlinear PDEs in sub-Riemannian spaces

The horizontal mean curvature flow is an evolution of a hypersurface, which is interesting not only in a theoretical framework but also in applied science, for example in neurogeometry and computer science (e.g. [13, 14, 15]). The associated equation, roughly speaking, describes the motion of a hypersurface embedded in a sub-Riemannian geometry (e.g. the Heisenberg group or a Carnot group, see [4, 43]) in relation to its horizontal mean curvature