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

We construct a new family of entire solutions to the Yamabe equation -Delta u = n(n-2)/4 vertical bar u vertical bar(4/n-2) u in D-1,D-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). (C) 2021 Elsevier Masson SAS. All rights reserved.

Automated summary

We construct a new family of entire solutions to the Yamabe equation, achieving maximal rank in odd dimensions for the first time. Our construction shows analogies with the doubling of equatorial spheres in the construction of minimal surfaces in S-3(1).