Rigidity of solitons of the Gauss curvature flow in Euclidean space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912488440725504 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | In this paper, we consider $λ$-translating solitons and $λ$-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only $λ$-translating solitons with constant mean curvature. We also prove that planes, spheres and circular cylinders are the only $λ$-shrinkers with constant mean curvature. We give a classification of the $λ$-translating solitons and $λ$-shrinkers with one constant principal curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of solitons of the Gauss curvature flow in Euclidean space López, Rafael Differential Geometry 53C44, 53C22 In this paper, we consider $λ$-translating solitons and $λ$-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only $λ$-translating solitons with constant mean curvature. We also prove that planes, spheres and circular cylinders are the only $λ$-shrinkers with constant mean curvature. We give a classification of the $λ$-translating solitons and $λ$-shrinkers with one constant principal curvature. |
| title | Rigidity of solitons of the Gauss curvature flow in Euclidean space |
| topic | Differential Geometry 53C44, 53C22 |
| url | https://arxiv.org/abs/2507.12863 |