PDE Seminar (2015/11/2): On the Horizontal Mean Curvature Flow Equation in the Heisenberg Group

Date
2015-11-2 16:45 - 2015-11-2 17:45
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Qing Liu (Fukuoka University)
 
The horizontal mean curvature flow in the Heisenberg group has important applications in the study of a cortical model of image completion. Using the level set formulation, we discuss uniqueness and existence of viscosity solutions to the horizontal mean curvature flow equation. Since this equation has a singularity stronger than its Euclidean counterpart, the uniqueness of solutions turns out to be a more challenging problem. In this talk, we focus on two special cases. We first talk about the mean curvature motion of surfaces that are rotationally symmetric with respect to the vertical axis. We then turn to the case of graph-like surfaces. Part of this talk is based on joint work with F. Ferrari and J. Manfredi.