Desingularization of Clifford torus and nonradial solutions to the Yamabe problem with maximal rank

Maria Medina, Monica Musso, Juncheng Wei

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Abstract

Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula presented]|u| [Formula presented] u,u∈D 1,2 (R n ). The case n=4 is the first example in the literature of a solution with maximal rank N=2n+1+[Formula presented].

Original languageEnglish
Pages (from-to)2470-2523
Number of pages54
JournalJournal of Functional Analysis
Volume276
Issue number8
Early online date13 Feb 2019
DOIs
Publication statusPublished - 15 Apr 2019

Keywords

  • Entire solutions
  • Gluing methods
  • Rigidity properties for entire solutions
  • Yamabe problem

ASJC Scopus subject areas

  • Analysis

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