We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate translating solitons that can be locally written as the product of two functions of one variable. We extend the results in Lorentz-Minkowski space.
Mean curvature flow, translating soliton, surfaces of translation, homothetical surface
AYDIN, MUHİTTİN EVREN and LOPEZ, RAFAEL
"Translating solitons of translation and homothetical types,"
Turkish Journal of Mathematics: Vol. 46:
8, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/13