Asymptotic behaviour of the weak inverse anisotropic mean curvature flow
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918227071729664 |
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| author | Gao, Chaoqun Wei, Yong Zhou, Rong |
| author_facet | Gao, Chaoqun Wei, Yong Zhou, Rong |
| contents | We first establish a local gradient estimate for anisotropic $p$-harmonic functions. A key feature of our estimate is that the constant remains bounded as $p\to 1$; consequently, in the limit $p\to 1$, this estimate yields the local gradient estimate for weak solutions of the inverse anisotropic mean curvature flow (IAMCF). As an application, we show that the weak IAMCF is asymptotic to the expanding Wulff shape solution at the infinity, thereby extending the result of Huisken and Ilmanen in [8] to the anisotropic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behaviour of the weak inverse anisotropic mean curvature flow Gao, Chaoqun Wei, Yong Zhou, Rong Differential Geometry We first establish a local gradient estimate for anisotropic $p$-harmonic functions. A key feature of our estimate is that the constant remains bounded as $p\to 1$; consequently, in the limit $p\to 1$, this estimate yields the local gradient estimate for weak solutions of the inverse anisotropic mean curvature flow (IAMCF). As an application, we show that the weak IAMCF is asymptotic to the expanding Wulff shape solution at the infinity, thereby extending the result of Huisken and Ilmanen in [8] to the anisotropic case. |
| title | Asymptotic behaviour of the weak inverse anisotropic mean curvature flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.08168 |