Geodesic
Low Complexity Solutions of the Allen–Cahn Equation on Three-spheres
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 287-291

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DOI

In this short note, we prove that on the three-sphere with any bumpy metric there exist at least two pairs of solutions of the Allen–Cahn equation with spherical interface and index at most two. The proof combines several recent results from the literature.
DOI : 10.4153/CMB-2018-033-4
Mots-clés : Allen–Cahn equation, phase transition, small index 
Haslhofer, Robert; Ivaki, Mohammad N. Low Complexity Solutions of the Allen–Cahn Equation on Three-spheres. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 287-291. doi: 10.4153/CMB-2018-033-4
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     author = {Haslhofer, Robert and Ivaki, Mohammad N.},
     title = {Low {Complexity} {Solutions} of the {Allen{\textendash}Cahn} {Equation} on {Three-spheres}},
     journal = {Canadian mathematical bulletin},
     pages = {287--291},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-033-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-033-4/}
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