On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group-Reference-Cited by-同舟云学术

On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group

Published:2014-05-26 Issue:03 Volume:16 Page:1350027
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Ferrari Fausto¹,Liu Qing²,Manfredi Juan J.²

Affiliation:

1. Dipartimento di Matematica dell'Università di Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199713500272

Reference29 articles.

1. Mean curvature flow through singularities for surfaces of rotation

2. A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature

3. Front Propagation and Phase Field Theory

4. ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP

5. Generalized Mean Curvature Flow in Carnot Groups

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