Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles

Abstract

In this work, we establish several rigidity results for spacelike self-shrinkers immersed in the pseudo-Euclidean space ${\mathbb{R}}_p^{n+p}$. Under suitable boundedness conditions on either the mean curvature vector or the second fundamental form, we apply different versions of Omori--Yau type maximum principles due to Qiu [20], Chen and Qiu [10], and Alías, Caminha, and Nascimento [3] to show that such self-shrinkers must be spacelike hyperplanes. These results contribute to the broader classification of spacelike self-shrinkers under natural geometric assumptions.