#### Vol. 314, No. 1, 2021

 Recent Issues Vol. 320: 1 Vol. 319: 1  2 Vol. 318: 1  2 Vol. 317: 1  2 Vol. 316: 1  2 Vol. 315: 1  2 Vol. 314: 1  2 Vol. 313: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
Uniformization theorems: Between Yamabe and Paneitz

### Cheikh Birahim Ndiaye, Yannick Sire and Liming Sun

Vol. 314 (2021), No. 1, 115–159
##### 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 $\gamma \in \left(0,1\right)$ 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 $\gamma \in \left(1,min\left\{2,\frac{n}{2}\right\}\right)$ provided the associated fractional GJMS operator satisfies the strong maximum principle.

##### Keywords
fractional GJMS operator, Poincaré–Einstein manifold, algebraic topological argument, barycenter technique
##### Mathematical Subject Classification
Primary: 58J05
Secondary: 35R11, 53A31