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• W2949390354 abstract "We prove that given a minimal hypersurface $Gamma$ in a compact Riemannian manifold $M$ without boundary, if all the Jacobi fields of $Gamma$ are generated by ambient isometries, then we can find solutions of the Allen-Cahn equation $-varepsilon^2Delta u +W'(u)=0$ on $M$, for sufficiently small $varepsilon>0$, whose nodal sets converge to $Gamma$. This extends the results of Pacard-Ritore (in the case of closed manifolds and zero mean curvature)." @default.
• W2949390354 created "2019-06-27" @default.
• W2949390354 creator A5020959419 @default.
• W2949390354 creator A5079775750 @default.
• W2949390354 date "2019-06-13" @default.
• W2949390354 modified "2023-09-27" @default.
• W2949390354 title "Solutions of the Allen-Cahn equation on closed manifolds in the presence of symmetry" @default.
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• W2949390354 hasPublicationYear "2019" @default.
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