Doubling nodal solutions to the Yamabe equation in Rn with maximal rank

Maria Medina, Monica Musso

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Abstract

We construct a new family of entire solutions to the Yamabe equation −Δu=[Formula presented]|u|[Formula presented]u in D1,2(Rn). If n=3 our solutions have maximal rank, being the first example in odd dimension. Our construction has analogies with the doubling of the equatorial spheres in the construction of minimal surfaces in S3(1).

Original languageEnglish
Pages (from-to)145-188
JournalJournal des Mathematiques Pures et Appliquees
Volume152
Early online date28 May 2021
DOIs
Publication statusPublished - 31 Aug 2021

Keywords

  • Lyapunov-Schmidt reduction
  • Maximal solutions
  • Yamabe problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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