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.
Capoga, L., Cittini, G., & Magnani, C. S. G. (2013). Sub-Riemannian heat kernels and mean curvature flow of graphs. Journal of Functional Analysis, 264(8), 1899-1928. https://doi.org/10.1016/j.jfa.2013.01.020
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This is a pre-print of an article published in the Journal of Functional Analysis. The final authenticated version is available online at: https://doi.org/10.1016/j.jfa.2013.01.020.