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arXiv · 2501.15812

Lawson cones and the Allen-Cahn equation

Oscar Agudelo·Matteo Rizzi
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Abstract

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 $-\Delta u=u-u^3$ in $\R^{N+1}$, $N+1\ge 8$, whose zero level set has exactly $k\ge 2$ connected components and with infinite Morse index.

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Oscar Agudelo, Matteo Rizzi. 2025-01-27. Lawson cones and the Allen-Cahn equation. https://arxiv.org/abs/2501.15812

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