We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 [42]) 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) [27] 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
Luca Capogna, Giovanna Citti, Cosimo Senni Guidotti Magnani (2013). Sub-Riemannian heat kernels and mean curvature flow of graphs. JOURNAL OF FUNCTIONAL ANALYSIS, 264, 1899-1928 [10.1016/j.jfa.2013.01.020].
Sub-Riemannian heat kernels and mean curvature flow of graphs
CITTI, GIOVANNA;SENNI GUIDOTTI MAGNANI, COSIMO
2013
Abstract
We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 [42]) 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) [27] 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 graphsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
