We prove existence and uniqueness for a two-parameter family of translators mean curvature flow. get additional examples by taking limits at the boundary parameter space. Some resemble well-known minimal surfaces (Scherk’s doubly periodic surfaces, helicoids), but others have no surface analogs. A one-parameter subfamily (the pitchforks) finite topology quadratic area growth, thus might arise a...

Abstract We consider the fractional mean curvature flow of entire Lipschitz graphs. provide regularity results, and we study long time asymptotics flow. In particular show that in a suitable rescaled framework, if initial graph is sublinear perturbation cone, evolution asymptotically approaches an expanding self-similar solution. also prove stability hyperplanes convex cones unrescaled setting.