A rigidity result for 2-dimensional λ-translators

Abstract

In this paper, we will develop a different technique to study the rigidity of complete $ \lambda $-translators $ x:M^{2} \rightarrow \mathbb R^{3} $ with the non-zero constant gauss curvature in the Euclidean space $ \mathbb R^{3} $.

Keywords

• second fundamental form
• $ \lambda $-translator
• gauss curvature
• non-umbilic points
• mean curvature