Arnold-Thom conjecture for the arrival time of surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913912495013888 |
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| author | Lee, Tang-Kai Zhu, Jingze |
| author_facet | Lee, Tang-Kai Zhu, Jingze |
| contents | Following Łojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for analytic functions. We prove Łojasiewicz's theorem and Arnold's conjecture in the context of arrival time functions for mean curvature flows in $\mathbb R^{n+1}$ with neck or non-degenerate cylindrical singularities. In particular, we prove the conjectures for all mean convex mean curvature flows of surfaces, including the cases when the arrival time functions are not $C^2.$ The results also apply to mean curvature flows starting from two-spheres or generic closed surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arnold-Thom conjecture for the arrival time of surfaces Lee, Tang-Kai Zhu, Jingze Differential Geometry Analysis of PDEs Following Łojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for analytic functions. We prove Łojasiewicz's theorem and Arnold's conjecture in the context of arrival time functions for mean curvature flows in $\mathbb R^{n+1}$ with neck or non-degenerate cylindrical singularities. In particular, we prove the conjectures for all mean convex mean curvature flows of surfaces, including the cases when the arrival time functions are not $C^2.$ The results also apply to mean curvature flows starting from two-spheres or generic closed surfaces. |
| title | Arnold-Thom conjecture for the arrival time of surfaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2405.19064 |