Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915747939221504 |
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| author | Ma, John Man Shun Muhammad, Ali Møller, Niels Martin |
| author_facet | Ma, John Man Shun Muhammad, Ali Møller, Niels Martin |
| contents | In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in $\mathbb{R}^{n+1}$. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_08641 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry Ma, John Man Shun Muhammad, Ali Møller, Niels Martin Differential Geometry 53E10 In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in $\mathbb{R}^{n+1}$. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry. |
| title | Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2202.08641 |