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arXiv · 1401.7071

Bifurcation of periodic solutions to the singular Yamabe problem on spheres

Renato G. Bettiol·Paolo Piccione·Bianca Santoro
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Abstract

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 $S^1$ inside $S^m$, $m\geq 5$, that are conformal to the round (incomplete) metric and "periodic" in the sense of being invariant under a discrete group of conformal transformations. These solutions come from bifurcating branches of constant scalar curvature metrics on compact quotients of $S^m \setminus S^1\cong S^{m-2}\times H^2$.

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Renato G. Bettiol, Paolo Piccione, Bianca Santoro. 2014-01-28. Bifurcation of periodic solutions to the singular Yamabe problem on spheres. https://doi.org/10.4310/jdg%2F1463404117

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