Lawson cones and the Allen-Cahn equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917903490613248 |
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| author | Agudelo, Oscar Rizzi, Matteo |
| author_facet | Agudelo, Oscar Rizzi, Matteo |
| contents | In this paper we discuss nondegeneracy and stability properties of some special minimal hypersurfaces which are asymptotic to a given Lawson cone $C_{m,n}$, for $m,\,n\ge 2$. Then we use such hypersurfaces to construct solutions to the Allen-Cahn equation $-Δu=u-u^3$ in $\R^{N+1}$, $N+1\ge 8$, whose zero level set has exactly $k\ge 2$ connected components and with infinite Morse index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lawson cones and the Allen-Cahn equation Agudelo, Oscar Rizzi, Matteo Differential Geometry Analysis of PDEs In this paper we discuss nondegeneracy and stability properties of some special minimal hypersurfaces which are asymptotic to a given Lawson cone $C_{m,n}$, for $m,\,n\ge 2$. Then we use such hypersurfaces to construct solutions to the Allen-Cahn equation $-Δu=u-u^3$ in $\R^{N+1}$, $N+1\ge 8$, whose zero level set has exactly $k\ge 2$ connected components and with infinite Morse index. |
| title | Lawson cones and the Allen-Cahn equation |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2501.15812 |