Complete $$\lambda $$-surfaces in $${\mathbb {R}}^3$$

Abstract

The purpose of this paper is to study complete \(\lambda \)-surfaces in Euclidean space \({\mathbb {R}}^3\). A complete classification for 2-dimensional complete \(\lambda \)-surfaces in Euclidean space \(\mathbb R^3\) with constant squared norm of the second fundamental form is given, which confirms a conjecture of Guang (Self-shrinkers and translating solitons of mean curvature flow, 2016, p 74).