A Bernstein type theorem for entire graphic 2-dimensional Λ-submanifolds in R⁴

Abstract

In this paper, we first recall the definition of Λ-submanifolds. Then we prove a Bernstein type result for 2-dimensional entire graphic Λ-submanifolds in R⁴. This theorem can be viewed as a generalization of Zhou's Bernstein type theorem for 2-dimensional self-shrinkers in R⁴.