Rigidity theorems of spacelike entire self-shrinking graphs in the pseudo-Euclidean space

Abstract

In this paper, we firstly establish a new volume growth estimate for spacelike entire graphs in the pseudo-Euclidean space ${\mathbb{R}}_n^{m+n}$. Then by using this volume growth estimate and the Co-Area formula, we prove various rigidity results for spacelike entire self-shrinking graphs.