Conformal Metrics with Prescribed Fractional Scalar Curvature on Conformal Infinities with Positive Fractional Yamabe Constants
- Authors
- Kim, Seunghyeok
- Issue Date
- Apr-2021
- Publisher
- SPRINGER
- Keywords
- Prescribed fractional scalar curvature problem; Fractional Yamabe problem; Existence; Regularity
- Citation
- JOURNAL OF GEOMETRIC ANALYSIS, v.31, no.4, pp.4287 - 4327
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF GEOMETRIC ANALYSIS
- Volume
- 31
- Number
- 4
- Start Page
- 4287
- End Page
- 4327
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/142141
- DOI
- 10.1007/s12220-020-00434-x
- ISSN
- 1050-6926
- Abstract
- Let (X, g(+)) be an asymptotically hyperbolic manifold with conformal infinity (M, [(h) over cap]). Our primary aim is to introduce the prescribed fractional scalar curvature problem on M and to provide its solutions under various geometric conditions on X and M. We also deduce the existence results for the fractional Yamabe problem in the end-point cases, e.g., n = 3, gamma = 1 2 and M is non-umbilic, etc. Finally, we prove that all solutions we find here are smooth on M.
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