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Low Complexity Solutions of the Allen–Cahn Equation on Three-spheres

  • Robert Haslhofer (a1) and Mohammad N. Ivaki (a1)
Abstract

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.

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R. H. was partially supported by NSERC grant RGPIN-2016-04331 and a Connaught New Researcher Award. M. I. was supported by a Marsden Postdoctoral Fellowship. Both authors thank the Fields Institute for providing an excellent research environment during the thematic program on Geometric Analysis.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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