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 Gonzalez 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 infinity for asymptotically hyperbolic metrics is required.

References in corpus (1)

• Sharp constants in weighted trace inequalities on Riemannian manifolds

Cited by in corpus (2)

• On perturbations of the fractional Yamabe problem
• Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings