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.
ON THE HORIZONTAL MEAN CURVATURE FLOW FOR AXISYMMETRIC SURFACES IN THE HEISENBERG GROUP / FAUSTO FERRARI; QING LIU; JUAN J. MANFREDI. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 16:(2014), pp. 1350027.1350027-1-1350027.1350027-41. [10.1142/S0219199713500272]
ON THE HORIZONTAL MEAN CURVATURE FLOW FOR AXISYMMETRIC SURFACES IN THE HEISENBERG GROUP
FERRARI, FAUSTO;
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
