Sub-riemannian Heat Kernels and Mean Curvature Flow of Graphs

Authors

Luca Capogna, University of Minnesota Twin CitiesFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna
Cosimo Senni Guidotti Magnani, Alma Mater Studiorum Università di Bologna

Document Type

Article

Publication Date

4-15-2013

Publication Title

Journal of Functional Analysis

Abstract

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 [42]) 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 (1993) [27] 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.

Keywords

Discrete time-step approximations, Heat kernels in Lie groups, Mean curvature flow, Nonlinear semi-groups

Volume

264

Issue

8

First Page

1899

Last Page

1928

DOI

10.1016/j.jfa.2013.01.020

ISSN

00221236

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Capogna, Luca; Citti, Giovanna; and Senni Guidotti Magnani, Cosimo, "Sub-riemannian Heat Kernels and Mean Curvature Flow of Graphs" (2013). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/134