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

Abstract We construct a new family of entire solutions to the Yamabe equation − Δ u = n ( n − 2 ) 4 | u | 4 n − 2 u  in  D 1 , 2 ( R n ) . 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 S 3 ( 1 ) .

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