Uniformization Theorems: Between Yamabe and Paneitz

Abstract

This paper is devoted to several existence results for a generalized version of the Yamabe problem. First, we prove the remaining global cases for the range of powers $\gamma \in (0,1)$ for the generalized Yamabe problem introduced by Gonzalez and Qing. Second, building on a new approach by Case and Chang for this problem, we prove that this Yamabe problem is solvable in the Poincaré-Einstein case for $\gamma \in (1,\min \{2,n/2\})$ provided the associated fractional GJMS operator satisfies the strong maximum principle.

References in corpus (5)

• Barycenter technique and the Riemann mapping problem of Escobar
• Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow
• Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
• Some energy inequalities involving fractional GJMS operators
• Fractional Yamabe problem on locally flat conformal infinities of Poincare-Einstein manifolds

Cited by in corpus (1)

• Asymptotics of the Poisson kernel and Green's functions of the fractional conformal Laplacian