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arXiv · 2302.11073

Multiplicity of singular solutions to the fractional Yamabe problem on spheres

Renato G. Bettiol·María del Mar González·Ali Maalaoui
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Abstract

We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on $S^n \setminus S^k$, using bifurcation techniques. These are singular (positive) solutions to a non-local equation with critical non-linearity.

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Renato G. Bettiol, María del Mar González, Ali Maalaoui. 2023-02-22. Multiplicity of singular solutions to the fractional Yamabe problem on spheres. https://doi.org/10.1016/j.jde.2024.01.019

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