Geometric Analysis Seminar
Speaker: Liming Sun (Johns Hopkins University)
Title: Some convexity theorems of translating solitons in the mean curvature flow.
Abs: I will be talking about the translating solitons (translators) in the mean curvature flow. Convexity theorems of translators play fundamental roles in the classification of them. Spruck and Xiao proved any two dimensional mean convex translator is actually convex. We proved a similar convex theorem for higher dimensional translators, namely the 2-convex translating solitons are actually convex. Our theorem implies 2-convex translating solitons have to be the bowl soliton. Our second theorem regards the solutions of the Dirichlet problem for translators in a bounded convex domain . We proved the solutions will be convex under appropriate conditions. This theorem implies the existence of n-2 family of locally strictly convex translators in higher dimension. In the end, we will show that our method could be used to establish a convexity theorem for constant mean curvature graph equation.
Thursday, January 9 at 5:00pm to 6:00pm
Ayres Hall, 111
1403 Circle Drive, Knoxville, TN 37996