Free boundary minimal Möbius band in spherical caps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911083581669376 |
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| author | Spezia, Mateus |
| author_facet | Spezia, Mateus |
| contents | We study compactly free boundary minimal submanifolds in spherical caps $\Br$ and their geometric spectral properties. Following the foundational work of Fraser-Schoen \cite{FS2012}, Lima-Menezes \cite{LM23} established the connection between free boundary minimal surfaces in spherical caps and spectral geometry. In this work, we present three main contributions: (1) We prove that any free boundary minimal Möbius band in $\Br$ immersed by first Steklov eigenfunctions must be intrinsically rotationally symmetric ; (2) We explicitly construct such a Möbius band in $\mathbb{B}^4(r)$ for $0<r<\fracπ{2}$; and (3) We generalize Morse index estimates for free boundary minimal submanifolds in spherical caps, showing that non totally geodesic immersions have index at least $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free boundary minimal Möbius band in spherical caps Spezia, Mateus Differential Geometry We study compactly free boundary minimal submanifolds in spherical caps $\Br$ and their geometric spectral properties. Following the foundational work of Fraser-Schoen \cite{FS2012}, Lima-Menezes \cite{LM23} established the connection between free boundary minimal surfaces in spherical caps and spectral geometry. In this work, we present three main contributions: (1) We prove that any free boundary minimal Möbius band in $\Br$ immersed by first Steklov eigenfunctions must be intrinsically rotationally symmetric ; (2) We explicitly construct such a Möbius band in $\mathbb{B}^4(r)$ for $0<r<\fracπ{2}$; and (3) We generalize Morse index estimates for free boundary minimal submanifolds in spherical caps, showing that non totally geodesic immersions have index at least $n$. |
| title | Free boundary minimal Möbius band in spherical caps |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.22332 |