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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.08728 |
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| _version_ | 1866909289447161856 |
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| author | Agudelo, Oscar Rizzi, Matteo |
| author_facet | Agudelo, Oscar Rizzi, Matteo |
| contents | In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in $\mathbb{R}^m\times \mathbb{R}^n$ with $m,n\geq 2$. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone $C_{m,n}$. In the case $m+n\ge 8$, we show that such hypersurfaces are strictly stable and we provide a full classification of their bounded Jacobi fields, which in turn allows us to prove the non-degeneracy of such surfaces. In the case $m+n\le 7$, we prove that such hypersurfaces have infinite Morse index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Jacobi operator of some special minimal hypersurfaces Agudelo, Oscar Rizzi, Matteo Differential Geometry In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in $\mathbb{R}^m\times \mathbb{R}^n$ with $m,n\geq 2$. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone $C_{m,n}$. In the case $m+n\ge 8$, we show that such hypersurfaces are strictly stable and we provide a full classification of their bounded Jacobi fields, which in turn allows us to prove the non-degeneracy of such surfaces. In the case $m+n\le 7$, we prove that such hypersurfaces have infinite Morse index. |
| title | The Jacobi operator of some special minimal hypersurfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.08728 |