Soliton to mean curvature flow

Time:

Venue/Location: C102, VIASM

Speaker: Prof. Juncheol Pyo (National Pusan University)

Abstract:

Mean curvature flow is that the hypersurface deforms in a normal direction and its speed equals the mean curvature at each point. It is well-known that any closed hypersurface occurs singularities in finite time under the mean curvature flow. These singularities distinguish into two types of hypersurfaces as blow-up models: translating solitons and self-similar solitons that are also special solutions to the flow. In this talk, we introduce some theorems for a translating soliton including any complete proper translating soliton can not be contained in a half-space opposite to the direction of a translating soliton under the mean curvature flow.