Minimal networks on balls and spheres for almost standard metrics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914650776403968 |
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| author | Sciaraffia, Luciano |
| author_facet | Sciaraffia, Luciano |
| contents | We study the existence of minimal networks in the unit sphere $\mathbf{S}^d$ and the unit ball $\mathbf{B}^d$ of $\mathbf{R}^d$ endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method, modelled on the configuration of $θ$-networks in $\mathbf{S}^d$ and triods in $\mathbf{B}^d$, jointly with the Lusternik--Schnirelmann category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal networks on balls and spheres for almost standard metrics Sciaraffia, Luciano Differential Geometry 53C22, 58E10 We study the existence of minimal networks in the unit sphere $\mathbf{S}^d$ and the unit ball $\mathbf{B}^d$ of $\mathbf{R}^d$ endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method, modelled on the configuration of $θ$-networks in $\mathbf{S}^d$ and triods in $\mathbf{B}^d$, jointly with the Lusternik--Schnirelmann category. |
| title | Minimal networks on balls and spheres for almost standard metrics |
| topic | Differential Geometry 53C22, 58E10 |
| url | https://arxiv.org/abs/2401.13134 |