|
|||||
 |
|
|
|
|
Existence theorems of
the fractional Yamabe problem
Seunghyeok Kim, Monica Musso and Juncheng Wei |
|
Vol. 11 (2018), No. 1, 75–113
|
Abstract |
|
Let be an asymptotically hyperbolic manifold and its conformal infinity. This paper is devoted to deducing several existence results of the fractional Yamabe problem on under various geometric assumptions on and . Firstly, we handle when the boundary has a point at which the mean curvature is negative. Secondly, we re-encounter the case when has zero mean curvature and satisfies one of the following conditions: nonumbilic, umbilic and a component of the covariant derivative of the Ricci tensor on is negative, or umbilic and nonlocally conformally flat. As a result, we replace the geometric restrictions given by González and Qing (2013) and González and Wang (2017) with simpler ones. Also, inspired by Marques (2007) and Almaraz (2010), we study lower-dimensional manifolds. Finally, the situation when is Poincaré–Einstein and is either locally conformally flat or 2-dimensional is covered under a certain condition on a Green’s function of the fractional conformal Laplacian. |
Keywords
fractional Yamabe problem, conformal geometry, existence
|
Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 35R11, 53A30
|
Milestones
Received: 22 March 2016
Revised: 10 May 2017
Accepted: 10 August 2017
Published: 17 September 2017
|
Authors |
| Seunghyeok Kim | |
| Department of Mathematics College of Natural Sciences Hanyang University Seoul South Korea |
|
| Monica Musso | |
| Facultad de Matemáticas Pontificia Universidad Católica de Chile Santiago Chile |
|
| Juncheng Wei | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
|
|
