Daehwan Kim

Half-space theorem for a translating soliton to mean curvature flow

Mean curvature flow is that the hypersurface deforms in a normal direction and its speed equals to 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 distinguishes 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 a half-space type theorem for a translating soliton, namely, 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.