Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911182514814976 |
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| author | Matinpour, Elham |
| author_facet | Matinpour, Elham |
| contents | We investigate the geometric constraints imposed by low Morse index on minimal surfaces with Y-singularities, focusing on the classification of those with Morse index one. Our rigidity result establishes a partial uniqueness theorem, highlighting the Y-catenoid as a distinguished example among complete, two-sided minimal surfaces in $\mathbb{R}^3$ with Y-singularities and Morse index one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$ Matinpour, Elham Differential Geometry We investigate the geometric constraints imposed by low Morse index on minimal surfaces with Y-singularities, focusing on the classification of those with Morse index one. Our rigidity result establishes a partial uniqueness theorem, highlighting the Y-catenoid as a distinguished example among complete, two-sided minimal surfaces in $\mathbb{R}^3$ with Y-singularities and Morse index one. |
| title | Rigidity of Minimal Surfaces with Y-singularities and low Morse Index in $\mathbb{R}^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.24154 |