Rotational symmetry of ancient solutions to fully nonlinear curvature flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929233851318272 |
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| author | Cogo, A. Lynch, S. Martínez, O. Vičánek |
| author_facet | Cogo, A. Lynch, S. Martínez, O. Vičánek |
| contents | We address the classification of ancient solutions to fully nonlinear curvature flows for hypersurfaces. Under natural conditions on the speed of motion we classify ancient solutions which are convex, noncollapsing, uniformly two-convex and noncompact. There are exactly two possibilities -- every such solution is either a self-similarly shrinking cylinder, or else is a rotationally symmetric translating soliton. For a large class of flows this yields a complete classification of the blow-up limits that can arise at a singularity of a solution which is compact, embedded and two-convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rotational symmetry of ancient solutions to fully nonlinear curvature flows Cogo, A. Lynch, S. Martínez, O. Vičánek Differential Geometry Analysis of PDEs 53E10 We address the classification of ancient solutions to fully nonlinear curvature flows for hypersurfaces. Under natural conditions on the speed of motion we classify ancient solutions which are convex, noncollapsing, uniformly two-convex and noncompact. There are exactly two possibilities -- every such solution is either a self-similarly shrinking cylinder, or else is a rotationally symmetric translating soliton. For a large class of flows this yields a complete classification of the blow-up limits that can arise at a singularity of a solution which is compact, embedded and two-convex. |
| title | Rotational symmetry of ancient solutions to fully nonlinear curvature flows |
| topic | Differential Geometry Analysis of PDEs 53E10 |
| url | https://arxiv.org/abs/2310.08301 |