Allard-Type Regularity for Varifolds with Prescribed Contact Angle
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929288734834688 |
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| author | Wang, Gaoming |
| author_facet | Wang, Gaoming |
| contents | Given a bounded $C^2$ domain in $\mathbb{R}^{n+1}$ and an integral $n$-rectifiable varifold $V$ with bounded first variation and bounded generalized mean curvature. Given a $C^1$ function $θ$ defined on the boundary of the domain with range $(0,π)$, we assume $V$ has prescribed contact angle $θ$ with $\partial Ω$ and the tangent cone of $V$ at a point $X \in \partial Ω$ is a half-hyperplane of density one. Then we can show that the support of $V$ is a $C^{1,γ}$ hypersurface with boundary near $X$ for some $γ\in (0,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Allard-Type Regularity for Varifolds with Prescribed Contact Angle Wang, Gaoming Differential Geometry Analysis of PDEs Given a bounded $C^2$ domain in $\mathbb{R}^{n+1}$ and an integral $n$-rectifiable varifold $V$ with bounded first variation and bounded generalized mean curvature. Given a $C^1$ function $θ$ defined on the boundary of the domain with range $(0,π)$, we assume $V$ has prescribed contact angle $θ$ with $\partial Ω$ and the tangent cone of $V$ at a point $X \in \partial Ω$ is a half-hyperplane of density one. Then we can show that the support of $V$ is a $C^{1,γ}$ hypersurface with boundary near $X$ for some $γ\in (0,1)$. |
| title | Allard-Type Regularity for Varifolds with Prescribed Contact Angle |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2403.17415 |