A characterization of the grim reaper cylinder

Abstract

In this article we prove that a connected and properly embedded translating soliton in ${\mathbb{R}}^3$ with uniformly bounded genus on compact sets which is $C^1$-asymptotic to two planes outside a cylinder, either is flat or coincides with the grim reaper cylinder.

32 pages, 11 figures, original result improved, to appear in Journal für die reine und angewandte Mathematik