A Zoo Of Translating Solitons On A Parallel Light-Like Direction In Minkowski 3-Space

We deal with solitons of the mean curvature flow. The definition of translating solitons on a light-like directionin Minkowski 3-space is introduced. Firstly, we classify those which are graphical, translation surfaces, obtaining space-like and time-like, entire and not entire, complete and incomplete examples. Among them, all our time-like examples are incomplete. The second family consists of those which are invariant by a 1-dimensional subgroup of parabolic motions, i.e., with light-like axis. The classification result implies that all examples of this second family have singularities. (C) 2021 Elsevier B.V. All rights reserved.