Bifurcation of periodic solutions to the singular Yamabe problem on spheres
Bifurcation of periodic solutions to the singular Yamabe problem on spheres
We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $\mathbb{S}^1$ inside $\mathbb{S}^m , m \geq 5$, that are conformal to the round (incomplete) metric and periodic …