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

2017/07/06 by Kim, Seunghyeok
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.01929

Abstract

Let (X, g⁺) be an asymptotically hyperbolic manifold and (M, [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, γ= 1/2 and M is non-umbilic, etc. Every solution we find turns out to be smooth on M.

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