Rigidity theorems of spacelike self-shrinkers in the pseudo-Euclidean space

Hongbing Qiu, Linlin Sun

Published 2019-10-17Version 1

In this paper, we show that any spacelike $m$-submanifold which is closed with respect to the Euclidean topology in the pseudo-Euclidean space $\mathbb{R}^{m+n}_n$ is an entire graph, then we establish a new volume growth estimate. As applications, by using this volume growth estimate and the Co-Area formula, we prove various rigidity results for spacelike entire self-shrinking graphs.