EXISTENCE THEOREMS OF THE FRACTIONAL YAMABE PROBLEM
- Authors
- Kim, Seunghyeok; Musso, Monica; Wei, Juncheng
- Issue Date
- 2018
- Publisher
- MATHEMATICAL SCIENCE PUBL
- Keywords
- fractional Yamabe problem; conformal geometry; existence
- Citation
- ANALYSIS & PDE, v.11, no.1, pp.75 - 113
- Indexed
- SCIE
SCOPUS
- Journal Title
- ANALYSIS & PDE
- Volume
- 11
- Number
- 1
- Start Page
- 75
- End Page
- 113
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/150868
- DOI
- 10.2140/apde.2018.11.75
- ISSN
- 2157-5045
- Abstract
- Let X be an asymptotically hyperbolic manifold and M its conformal infinity. This paper is devoted to deducing several existence results of the fractional Yamabe problem on M under various geometric assumptions on X andM. Firstly, we handle when the boundary M has a point at which the mean curvature is negative. Secondly, we re-encounter the case when M 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 (X) over bar is negative, or umbilic and nonlocally conformally flat. As a result, we replace the geometric restrictions given by Gonzalez and Qing (2013) and Gonzalez and Wang (2017) with simpler ones. Also, inspired by Marques (2007) and Almaraz (2010), we study lower-dimensional manifolds. Finally, the situation when X is Poincare-Einstein and M is either locally conformally flat or 2-dimensional is covered under a certain condition on a Green's function of the fractional conformal Laplacian.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/150868)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.