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Seminar
FIELD Math:Geometry
DATE February 22 (Mon), 2021
TIME 15:10-16:10
PLACE Online
SPEAKER Kim, Daehwan
HOST Shin, Jinwoo
INSTITUTE 대구대학교
TITLE Half-space type theorem of translating solitons for mean curvature flow
ABSTRACT Flows related to the mean curvature have been studied extensively in differential geometry. Mean curvature flow is that the hypersurface deforms in a normal direction and its speed equals to the mean curvature at each point . The translating soliton is not only a eternal solution of the flow, which moves only to a constant direction under the mean curvature flow, but also a type of models for singularities. In the other point of view, it seems to be a minimal surface in conformally changed space of Euclidean space and we observe a similar property compare to half-space theorem of minimal surfaces. We define a half-space as one of the two parts into which a hyperplane divides R^(n+1) and prove that if a hyperplane s not parallel to the direction of the translation for translating solitons under the mean curvature flow, then complete translating solitons can be contained in a half-space whose boundary is the hyperplane, whereas the other half-space cannot contain the complete translating solitons.
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