EXISTENCE THEOREMS OF THE FRACTIONAL YAMABE PROBLEM
- Title
- EXISTENCE THEOREMS OF THE FRACTIONAL YAMABE PROBLEM
- Author
- 김승혁
- Keywords
- fractional Yamabe problem; conformal geometry; existence
- Issue Date
- 2018-01
- Publisher
- MATHEMATICAL SCIENCE PUBL
- Citation
- ANALYSIS & PDE, v. 11, no. 1, page. 75-113
- 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.
- URI
- https://msp.org/apde/2018/11-1/p02.xhtmlhttps://repository.hanyang.ac.kr/handle/20.500.11754/117273
- ISSN
- 1948-206X
- DOI
- 10.2140/apde.2018.11.75
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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