ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Luca Capogna (University of Arkansas)
A mean curvature flow in the Heisenberg group

Abstract: We discuss some very basic results concerning the gradient flow of the perimeter of a surface in the first Heisenberg group. Such flow is a sub-Riemannian analogue of the classical mean curvature flow and the corresponding nonlinear PDE is doubly degenerate. The focus of this talk will be on examples and characterizations of homothetic solutions, and on the relation between the mean curvature flow and legendrian foliations. This is joint work with Mario Bonk (Michigan).