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. - STAMPA. - 126:(2015), pp. 10521.437-10521.450. [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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
