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

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].