Fat equator effect and Minimality in immersions and submersions of the Sphere
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929331690799104 |
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| author | Garcia, Vicent Gimeno i Palmer, Vicente |
| author_facet | Garcia, Vicent Gimeno i Palmer, Vicente |
| contents | Inspired by the equatorial concentration of measure phenomenon in the sphere, a result which is deduced from the general, (and intrinsic), concentration of measure in $\mathbb{S}^n(1)$, we describe in this paper an equatorial concentration of measure satisfied by the closed, (compact without boundary), isometric and minimal immersions $x:Σ^m \rightarrow \mathbb{S}^n(1)$, ($m \leq n$), and by the minimal Riemannian submersions $π: Σ^m \rightarrow \mathbb{S}^n(1)$, ($m \geq n$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fat equator effect and Minimality in immersions and submersions of the Sphere Garcia, Vicent Gimeno i Palmer, Vicente Differential Geometry 58C35, 49Q15, 53A10 Inspired by the equatorial concentration of measure phenomenon in the sphere, a result which is deduced from the general, (and intrinsic), concentration of measure in $\mathbb{S}^n(1)$, we describe in this paper an equatorial concentration of measure satisfied by the closed, (compact without boundary), isometric and minimal immersions $x:Σ^m \rightarrow \mathbb{S}^n(1)$, ($m \leq n$), and by the minimal Riemannian submersions $π: Σ^m \rightarrow \mathbb{S}^n(1)$, ($m \geq n$). |
| title | Fat equator effect and Minimality in immersions and submersions of the Sphere |
| topic | Differential Geometry 58C35, 49Q15, 53A10 |
| url | https://arxiv.org/abs/2404.19416 |