Stability of cylinders in $\mathbb{E}(κ,τ)$ homogeneous spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913420855476224 |
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| author | Bueno, Antonio López, Rafael |
| author_facet | Bueno, Antonio López, Rafael |
| contents | We extend the classical Plateau-Rayleigh instability criterion in the $\mathbb{E}(κ,τ)$ spaces. We prove the existence of a positive number $L_0>0$ such that if a truncated circular cylinder of radius $ρ$ in $\mathbb{E}(κ,τ)$ has length $L>L_0$ then it is unstable. This number $L_0$ depends on $κ$, $τ$ and $ρ$. The value $L_0$ is sharp under axially-symmetric variations of the surface. We also extend this result for the partitioning problem in $\mathbb{E}(κ,τ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of cylinders in $\mathbb{E}(κ,τ)$ homogeneous spaces Bueno, Antonio López, Rafael Differential Geometry 53A10, 53C42 We extend the classical Plateau-Rayleigh instability criterion in the $\mathbb{E}(κ,τ)$ spaces. We prove the existence of a positive number $L_0>0$ such that if a truncated circular cylinder of radius $ρ$ in $\mathbb{E}(κ,τ)$ has length $L>L_0$ then it is unstable. This number $L_0$ depends on $κ$, $τ$ and $ρ$. The value $L_0$ is sharp under axially-symmetric variations of the surface. We also extend this result for the partitioning problem in $\mathbb{E}(κ,τ)$. |
| title | Stability of cylinders in $\mathbb{E}(κ,τ)$ homogeneous spaces |
| topic | Differential Geometry 53A10, 53C42 |
| url | https://arxiv.org/abs/2407.05668 |