The isoperimetric inequality for the capillary energy outside convex cylinders
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915499725553664 |
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| author | Fusco, Nicola Julin, Vesa Morini, Massimiliano |
| author_facet | Fusco, Nicola Julin, Vesa Morini, Massimiliano |
| contents | We study the isoperimetric problem for capillary surfaces with a general contact angle $θ\in (0, π)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritoré relative isoperimetric inequality, corresponding to the case $θ= π/2$, to general angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The isoperimetric inequality for the capillary energy outside convex cylinders Fusco, Nicola Julin, Vesa Morini, Massimiliano Analysis of PDEs We study the isoperimetric problem for capillary surfaces with a general contact angle $θ\in (0, π)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritoré relative isoperimetric inequality, corresponding to the case $θ= π/2$, to general angles. |
| title | The isoperimetric inequality for the capillary energy outside convex cylinders |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.19011 |