Mean curvature flow translators with prescribed ends

Abstract: Mean curvature flow is the fastest way to decrease the area of surfaces. It is the model in many disciplines such as material science, fluid mechanism, and computer graphics. The translators are a special type of mean curvature flow soliton. They are the singularity model of mean curvature flow and they play an important role in Ilmanen's elliptic regularization construction of weak mean curvature flow. I will present my recent work with Zhihan Wang (The University of Chicago) on the construction of translators with prescribed ends.