Sub-Riemannian heat kernels and mean curvature flow of graphs

2012/08/30 by Capogna, Luca, Citti, Giovanna, Magnani, Cosimo Senni Guidotti
#35H20 #35K67 #35K93 #53C17 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1208.6211

Abstract

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher diffusion driven algorithm and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L. C. Evans in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graphs.

Related

• Generalized mean curvature flow in Carnot groups
• Regularity of mean curvature flow of graphs on Lie groups free up to step 2
• Mean curvature flow of an entire graph evolving away from the heat flow
• Horizontal Gauss Curvature Flow of Graphs in Carnot Groups
• A diffusion driven curvature flow