# 筑波大学微分幾何学火曜セミナー

Abstract: A translator is a surface in $\mathbb{R}^3$ that (up to a tangential diffeomorphism) moves  with velocity $v=(0,0,-1)$ by Mean Curvature Flow. Equivalently, the mean curvature at each  point is $H= (0,0,-1)^{\perp}.$ Besides vertical planes, one of the simplest examples of complete translators is the grim reaper cylinder. In this talk we will describe several existence and uniqueness results for complete translators which are graphs over planar domains. This is a joint work with D. Hoffman, T. Ilmanen and B. White.