Uniformization theorems: Between Yamabe and Paneitz

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 $γ \in (0, 1)$ 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 $γ \in (1, min {2, \frac{n}{2}})$ provided the associated fractional GJMS operator satisfies the strong maximum principle.

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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

Vol. 314, No. 1, 2021

Cheikh Birahim Ndiaye, Yannick Sire and Liming Sun

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors