Generalized mean curvature flow in Carnot groups

Abstract

In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting by Evans-Spruck and Chen-Giga-Goto. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.

References in corpus (2)

• The Bernstein Problem in the Heisenberg Group
• Constant mean curvature surfaces in sub-Riemannian geometry