Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants

Seunghyeok Kim

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arXiv · 1707.01929

Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants

Seunghyeok Kim

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Abstract

Let $(X, g^+)$ be an asymptotically hyperbolic manifold and $(M, [\hat{h}])$ its conformal infinity. Our primary aim in this paper is to introduce the prescribed fractional scalar curvature problem on $M$ and provide solutions under various geometric conditions on $X$ and $M$. We also obtain the existence results for the fractional Yamabe problem in the endpoint case, e.g., $n = 3$, $\gamma = 1/2$ and $M$ is non-umbilic, etc. Every solution we find turns out to be smooth on $M$.

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Seunghyeok Kim. 2017-07-06. Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants. https://arxiv.org/abs/1707.01929

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