Document Type
Article
Publication Date
8-1-2009
Publication Title
Communications in Partial Differential Equations
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.
Keywords
Carnot groups, Mean curvature flow, Sub-Riemannian geometry
Volume
34
Issue
8
First Page
937
Last Page
956
DOI
10.1080/03605300903050257
ISSN
03605302
Recommended Citation
Capogna, Luca and Citti, Giovanna, "Generalized Mean Curvature Flow in Carnot Groups" (2009). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/140
Comments
Peer reviewed accepted manuscript.