Ruled Surfaces of Generalized Self-Similar Solutions of the Mean Curvature Flow

Abstract

In Euclidean space, we investigate surfaces whose mean curvature H satisfies the equation H = alpha N, x + lambda, where N is the Gauss map, x is the position vector, and a and. are two constants. There surfaces generalize self-shrinkers and self-expanders of the mean curvature flow. We classify the ruled surfaces and the translation surfaces, proving that they are cylindrical surfaces.