We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics σ_ε collapsing to a subRiemannian metric σ as ε → 0. We establish C^(k,α) estimates for this flow, that are uniform as ε → 0 and as a consequence prove long time existence for the sub Riemannian mean curvature flow of the graph.
Capogna, L., Citti, G., Manfredini, M. (2015). Regularity of mean curvature flow of graphs on Lie groups free up to step 2. NONLINEAR ANALYSIS, 126, 437-450 [10.1016/j.na.2015.05.008].
Regularity of mean curvature flow of graphs on Lie groups free up to step 2
CITTI, GIOVANNA;MANFREDINI, MARIA
2015
Abstract
We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics σ_ε collapsing to a subRiemannian metric σ as ε → 0. We establish C^(k,α) estimates for this flow, that are uniform as ε → 0 and as a consequence prove long time existence for the sub Riemannian mean curvature flow of the graph.File in questo prodotto:
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