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.

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.

Creator

• Magnani, Cosimo
• Capogna, Luca
• Citti, Giovanna

Keyword

• Heat Kernels in Lie Groups
• Nonlinear Semi-Groups
• Mean Curvature Flow
• Discrete Time-Step Approximations

Date created

• 2/8/13

Resource type

• Article

Extent

• 30 pages

Source

• https://doi.org/10.1016/j.jfa.2013.01.020

Rights statement

• In Copyright

Last modified

• 2020-09-22