Doubling nodal solutions to the Yamabe equation in $\mathbb{R}^n$ with maximal rank

Abstract: We construct a new family of entire solutions to the Yamabe equation $$-\Delta u=\frac{n(n-2)}{4}|u|^{{\frac{4}{n-2}}u} \mbox{ in }\mathcal{D}<sup>{1,2}(\mathbb{R}<sup>n).$$ 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 $S<sup>3(1)$.