Invariant translators of the Solvable group

Abstract

We classify the translators to the mean curvature flow in the three-dimensional solvable group $So{l}_3$ that are invariant under the action of a one-parameter group of isometries of the ambient space. In particular we show that $So{l}_3$ admits graphical translators defined on a half-plane, in contrast with a rigidity result of Shahriyari for translators in the Euclidean space. Moreover we exhibit some non-existence results.

18 pages, 7 figures, some typos have been corrected in the second version