Let (X, g+) be an asymptotically hyperbolic manifold with conformal infinity (M, [h^]). Our primary aim is to introduce the prescribed fractional scalar curvature problem on M and to provide its solutions under various geometric conditions on X and M. We also deduce the existence results for the fractional Yamabe problem in the end-point cases, e.g., n= 3 , γ=12 and M is non-umbilic, etc. Finally, we prove that all solutions we find here are smooth on M.
- Fractional Yamabe problem
- Prescribed fractional scalar curvature problem