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arXiv · 2001.03548

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

Maria Medina·Monica Musso
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Abstract

We construct a new family of entire solutions to the Yamabe equation $$-\Delta u=\frac{n(n-2)}{4}|u|^{\frac{4}{n-2}}u \mbox{ in }\mathcal{D}^{1,2}(\mathbb{R}^n).$$ 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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Maria Medina, Monica Musso. 2020-01-10. Doubling nodal solutions to the Yamabe equation in $\mathbb{R}^n$ with maximal rank. https://arxiv.org/abs/2001.03548

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