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The Allen-Cahn equation and general minimal cones
We construct solutions to the Allen-Cahn equation $Δu+u-u^3=0$ in $\mathbb{R}^{N+1}$, with $N\ge 3$, whose zero level set is asymptotic (at infinity) to a given minimal cone. Our construction is quite general, since we only use a suitable nondegeneracy assumption; neither stability nor symmetry of t
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