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

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).