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Interface foliation near a minimal isoparametric hypersurface for the Allen-Cahn equation
Let $(M,g)$ be a closed Riemannian manifold of positive Ricci curvature. Let $f$ be a proper isoparametric function on $M$, and $Γ$ the unique level set of $f$ which is a minimal hypersurface. For any positive integer $k$, and $λ>0$ large enough, we construct a solution of the Allen-Cahn equation $
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