Journal of Functional Analysis
We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 ) and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L.C. Evans (1993)  in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graphs.
Discrete time-step approximations, Heat kernels in Lie groups, Mean curvature flow, Nonlinear semi-groups
Capogna, Luca; Citti, Giovanna; and Senni Guidotti Magnani, Cosimo, "Sub-riemannian Heat Kernels and Mean Curvature Flow of Graphs" (2013). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.