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.
Regularity of mean curvature flow of graphs on Lie groups free up to step 2 / Capogna, Luca; Citti, Giovanna; Manfredini, Maria. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 126:(2015), pp. 437-450. [10.1016/j.na.2015.05.008]
Regularity of mean curvature flow of graphs on Lie groups free up to step 2
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.
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