Torus action on Sn and sign-changing solutions for conformally invariant equations

Manuel Del Pino, Monica Musso, Frank Pacard, Angela Pistoia

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We construct sequences of sign-changing solutions for some conformally invariant semilinear elliptic equation which is defined Sn, when n ≥ 4. The solutions we obtain have large energy and concentrate along some special submanifolds of Sn. For example, for n ≥ 4 we obtain sequences of solutions whose energy concentrates along one great circle or finitely many great circles which are linked to each other (and they correspond to Hopf links embedded in S3 × {0} ⊂ Sn). In dimension n ≥ 5 we obtain sequences of solutions whose energy concentrates along a two-dimensional torus (which corresponds to a Clifford torus embedded in S3 × {0} ⊂ Sn).

Original languageEnglish
Pages (from-to)209-237
Number of pages29
JournalAnnali della Scuola Normale - Classe di Scienze
Volume12
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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