On the horizontal Mean Curvature Flow for Axisymmetric surfaces in the Heisenberg Group

Abstract

We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group.

References in corpus (1)

• Tug-of-war and the infinity Laplacian

Cited by in corpus (4)

• Uniqueness of viscosity mean curvature flow solution in two sub-Riemannian structures
• A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow
• A family of MCF solutions for the Heisenberg Group
• On viscosity and equivalent notions of solutions for anisotropic geometric equations