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arXiv · 1208.6211

Sub-Riemannian heat kernels and mean curvature flow of graphs

Luca Capogna·Giovanna Citti·Cosimo Senni Guidotti Magnani
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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.

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Luca Capogna, Giovanna Citti, Cosimo Senni Guidotti Magnani. 2013-01-19. Sub-Riemannian heat kernels and mean curvature flow of graphs. https://arxiv.org/abs/1208.6211

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