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 in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.
L. Capogna, G. Citti (2009). Generalized Mean Curvature Flow in Carnot Groups. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 34, 937-956 [10.1080/03605300903050257].
Generalized Mean Curvature Flow in Carnot Groups
CITTI, GIOVANNA
2009
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 in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.File in questo prodotto:
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