The structure of translating surfaces with finite total curvature

In this paper, we prove that any mean curvature flow translator sigma(2) subset of R-3 with finite total curvature and one end must be a plane. We also prove that if the translator sigma has multiple ends, they are asymptotic to a plane Pi containing the direction of translation and can be written as graphs over Pi. Finally, we determine that the ends of sigma are strongly asymptotic to Pi and obtain quantitative estimates for their asymptotic behavior.