Vol. 314, No. 1, 2021

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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 γ (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 γ (1,min{2, n 2 }) 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
Milestones
Received: 24 July 2020
Revised: 24 May 2021
Accepted: 9 July 2021
Published: 15 October 2021
Authors
Cheikh Birahim Ndiaye
Department of Mathematics
Howard University
Washington, DC
United States
Yannick Sire
Department of Mathematics
Johns Hopkins University
Baltimore, MD
United States
Liming Sun
Department of Mathematics
Academy of Mathematics and Systems Science
the Chinese Academy of Sciences
Beijing
China