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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.10200 |
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| _version_ | 1866916963138142208 |
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| author | Fusco, N. Julin, V. Morini, M. Pratelli, A. |
| author_facet | Fusco, N. Julin, V. Morini, M. Pratelli, A. |
| contents | We study the isoperimetric problem for capillary hypersurfaces with a general contact angle $θ\in (0, π)$, outside arbitrary convex sets. We prove that the capillary energy of any surface supported on any such convex set is larger than that of a spherical cap with the same volume and the same contact angle on a flat support, and we characterize the equality cases. This provides a complete solution to the isoperimetric problem for capillary surfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe-Ghomi-Ritoré inequality, which corresponds to the case $θ=\frac\pi2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The isoperimetric inequality for the capillary energy outside convex sets Fusco, N. Julin, V. Morini, M. Pratelli, A. Analysis of PDEs We study the isoperimetric problem for capillary hypersurfaces with a general contact angle $θ\in (0, π)$, outside arbitrary convex sets. We prove that the capillary energy of any surface supported on any such convex set is larger than that of a spherical cap with the same volume and the same contact angle on a flat support, and we characterize the equality cases. This provides a complete solution to the isoperimetric problem for capillary surfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe-Ghomi-Ritoré inequality, which corresponds to the case $θ=\frac\pi2$. |
| title | The isoperimetric inequality for the capillary energy outside convex sets |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.10200 |