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 (3)

• Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
• Sharp constants in weighted trace inequalities on Riemannian manifolds
• Scattering Matrix in Conformal Geometry

Cited by in corpus (5)

• A non-compactness result on the fractional Yamabe problem in large dimensions
• On perturbations of the fractional Yamabe problem
• Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings
• On local behavior of singular positive solutions to nonlocal elliptic equations
• Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents