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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12196 |
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| _version_ | 1866913995344052224 |
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| author | Barboza, Weiller F. Chaves |
| author_facet | Barboza, Weiller F. Chaves |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles Barboza, Weiller F. Chaves Differential Geometry 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 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. |
| title | Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.12196 |