Ancient mean curvature flows with finite total curvature
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911862958850048 |
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| author | Choi, Kyeongsu Huang, Jiuzhou Lee, Taehun |
| author_facet | Choi, Kyeongsu Huang, Jiuzhou Lee, Taehun |
| contents | We construct an $I$-family of ancient graphical mean curvature flows over a minimal hypersurface in $\mathbb{R}^{n+1}$ of finite total curvature with the Morse index $I$ by establishing exponentially fast convergence in terms of $|x|^2-t$. As a corollary, we show that these ancient flows have finite total curvature and finite mass drop. Moreover, one family of these flows is mean convex by a pointwise estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ancient mean curvature flows with finite total curvature Choi, Kyeongsu Huang, Jiuzhou Lee, Taehun Differential Geometry Analysis of PDEs We construct an $I$-family of ancient graphical mean curvature flows over a minimal hypersurface in $\mathbb{R}^{n+1}$ of finite total curvature with the Morse index $I$ by establishing exponentially fast convergence in terms of $|x|^2-t$. As a corollary, we show that these ancient flows have finite total curvature and finite mass drop. Moreover, one family of these flows is mean convex by a pointwise estimate. |
| title | Ancient mean curvature flows with finite total curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2405.01062 |