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June 2016 Bifurcation of periodic solutions to the singular Yamabe problem on spheres
Renato G. Bettiol, Paolo Piccione, Bianca Santoro
J. Differential Geom. 103(2): 191-205 (June 2016). DOI: 10.4310/jdg/1463404117

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 $\mathbb{S}^1$ inside $\mathbb{S}^m , m \geq 5$, 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 $\mathbb{S}^m \setminus \mathbb{S}^1 \cong \mathbb{S}^{m-2} \times \mathbb{H}^2$.

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Renato G. Bettiol. Paolo Piccione. Bianca Santoro. "Bifurcation of periodic solutions to the singular Yamabe problem on spheres." J. Differential Geom. 103 (2) 191 - 205, June 2016. https://doi.org/10.4310/jdg/1463404117

Information

Published: June 2016
First available in Project Euclid: 16 May 2016

zbMATH: 1348.53044
MathSciNet: MR3504948
Digital Object Identifier: 10.4310/jdg/1463404117

Rights: Copyright © 2016 Lehigh University

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Vol.103 • No. 2 • June 2016
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