Capillary curvature images
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918025140109312 |
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| author | Hu, Yingxiang Ivaki, Mohammad N. |
| author_facet | Hu, Yingxiang Ivaki, Mohammad N. |
| contents | In this paper, we solve the even capillary $L_p$-Minkowski problem for the range $-n < p < 1$ and $θ\in (0,\fracπ{2})$. Our approach is based on an iterative scheme that builds on the solution to the capillary Minkowski problem (i.e., the case $p = 1$) and leverages the monotonicity of a class of functionals under a family of capillary curvature image operators. These operators are constructed so that their fixed points, whenever they exist, correspond precisely to solutions of the capillary $L_p$-Minkowski problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Capillary curvature images Hu, Yingxiang Ivaki, Mohammad N. Differential Geometry Analysis of PDEs Metric Geometry In this paper, we solve the even capillary $L_p$-Minkowski problem for the range $-n < p < 1$ and $θ\in (0,\fracπ{2})$. Our approach is based on an iterative scheme that builds on the solution to the capillary Minkowski problem (i.e., the case $p = 1$) and leverages the monotonicity of a class of functionals under a family of capillary curvature image operators. These operators are constructed so that their fixed points, whenever they exist, correspond precisely to solutions of the capillary $L_p$-Minkowski problem. |
| title | Capillary curvature images |
| topic | Differential Geometry Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/2505.12921 |