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EnglishWe 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
| Titolo: | Sub-Riemannian heat kernels and mean curvature flow of graphs | |
| Autore/i: | Luca Capogna; CITTI, GIOVANNA; SENNI GUIDOTTI MAGNANI, COSIMO | |
| Autore/i Unibo: | ||
| Anno: | 2013 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jfa.2013.01.020 | |
| 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 graphs | |
| Data prodotto definitivo in UGOV: | 2013-06-29 13:14:24 | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/154331
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