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

TL;DR

This paper establishes volume growth estimates and rigidity theorems for spacelike entire self-shrinking graphs in pseudo-Euclidean spaces, advancing understanding of their geometric properties and constraints.

Contribution

It introduces new volume growth estimates and applies them to prove rigidity results for spacelike entire self-shrinking graphs in pseudo-Euclidean spaces.

Findings

Volume growth estimates for spacelike entire graphs

Rigidity results for self-shrinking graphs

Application of Co-Area formula in pseudo-Euclidean geometry

Abstract

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