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arXiv · 2508.12196

Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles

Weiller F. Chaves Barboza
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Abstract

In this work, we establish several rigidity results for spacelike self-shrinkers immersed in the pseudo-Euclidean space $\mathbb{R}^{n+p}_p$. 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 Al\'ias, 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.

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BibTeXRIS

Weiller F. Chaves Barboza. 2025-08-17. Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles. https://arxiv.org/abs/2508.12196

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