The Anisotropic Capillary $L_p$-Minkowski Problem
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911476039548928 |
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| author | Ding, Shanwei Gao, Jinyu Li, Guanghan Liu, Mengliang |
| author_facet | Ding, Shanwei Gao, Jinyu Li, Guanghan Liu, Mengliang |
| contents | This paper introduces the \textit{anisotropic $ω_0$-capillary $p$-sum} of two hypersurfaces in $\mathbb{R}_+^{n+1}$, and establishes a theory for anisotropic capillary convex bodies. For a smooth convex hypersurface $Σ$ with anisotropic $ω_0$-capillary boundary, we compute the variation of its anisotropic capillary $k$-th quermassintegral via this $p$-sum, thereby defining the associated anisotropic $ω_0$-capillary $k$-th $p$-surface area measure on the capillary Wulff shape $\mathcal{C}_{ω_{0}}$. This motivates us to propose and solve the anisotropic capillary $L_{p}$-Minkowski problem for $p\geq1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01066 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Anisotropic Capillary $L_p$-Minkowski Problem Ding, Shanwei Gao, Jinyu Li, Guanghan Liu, Mengliang Differential Geometry 53C65, 35J66, 53C42, 35J60, 53C45 This paper introduces the \textit{anisotropic $ω_0$-capillary $p$-sum} of two hypersurfaces in $\mathbb{R}_+^{n+1}$, and establishes a theory for anisotropic capillary convex bodies. For a smooth convex hypersurface $Σ$ with anisotropic $ω_0$-capillary boundary, we compute the variation of its anisotropic capillary $k$-th quermassintegral via this $p$-sum, thereby defining the associated anisotropic $ω_0$-capillary $k$-th $p$-surface area measure on the capillary Wulff shape $\mathcal{C}_{ω_{0}}$. This motivates us to propose and solve the anisotropic capillary $L_{p}$-Minkowski problem for $p\geq1$. |
| title | The Anisotropic Capillary $L_p$-Minkowski Problem |
| topic | Differential Geometry 53C65, 35J66, 53C42, 35J60, 53C45 |
| url | https://arxiv.org/abs/2603.01066 |