Generalized Mean Curvature Flow in Carnot Groups

Authors

Luca Capogna, University of ArkansasFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna

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

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Capogna, Luca and Citti, Giovanna, "Generalized Mean Curvature Flow in Carnot Groups" (2009). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/140