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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.09104 |
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| _version_ | 1866916948576567296 |
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| author | Perdomo, Oscar |
| author_facet | Perdomo, Oscar |
| contents | Recently, for any n>1, Carlotto and Schulz showed the existence of a minimal embedding in the 2n-dimensional unit sphere. In this paper, we show that the stability index of these embedded minimal hypersurfaces is at least n^2+4n+3. We also show that Yau's conjecture holds for these examples if and only if the solution of the differential equation z''(t)+a_n(t)z'(t)+(2n-1)z(t)=0 with z(0)=1 and z'(0)=0 satisfies z'(T)>0. Here,T and the T-periodic function a_n(t) are determined in terms of the functions defining the minimal immersion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori Perdomo, Oscar Differential Geometry 53C42, 58J50 Recently, for any n>1, Carlotto and Schulz showed the existence of a minimal embedding in the 2n-dimensional unit sphere. In this paper, we show that the stability index of these embedded minimal hypersurfaces is at least n^2+4n+3. We also show that Yau's conjecture holds for these examples if and only if the solution of the differential equation z''(t)+a_n(t)z'(t)+(2n-1)z(t)=0 with z(0)=1 and z'(0)=0 satisfies z'(T)>0. Here,T and the T-periodic function a_n(t) are determined in terms of the functions defining the minimal immersion. |
| title | The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori |
| topic | Differential Geometry 53C42, 58J50 |
| url | https://arxiv.org/abs/2508.09104 |