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 σϵ collapsing to a subRiemannian metric σ0 as ϵ→0. We establish Ck,α estimates for this flow, that are uniform as ϵ→0 and as a consequence prove long time existence for the subRiemannian mean curvature flow of the graph. Our proof extend to the setting of every step two Carnot group (not necessarily free) and can be adapted following our previous work in Capogna et al. (2013) to the total variation flow.

Creator

• Citti, Giovanna
• Manfredini, Maria
• Capogna, Luca

Keyword

• Sub-Riemannian Geometry
• Mean Curvature Flow
• Carnot Groups

Date created

• 6/5/15

Resource type

• Article

Extent

• 14 pages

Source

• https://doi.org/10.1016/j.na.2015.05.008

Rights statement

• In Copyright

Last modified

• 2020-09-22