Further results on the fractional Yamabe problem: the umbilic case

Abstract

We prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonz alez and Qing. These are inspired by the work of Coda-Marques on the boundary Yamabe problem but, in addition, a careful understanding of the behavior at in nity for asymptotically hyperbolic metrics is required