A non-compactness result on the fractional Yamabe problem in large dimensionsopen access
- Authors
- Kim, Seunghyeok; Musso, Monica; Wei, Juncheng
- Issue Date
- Dec-2017
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Fractional Yamabe problem; Blow-up analysis
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.273, no.12, pp.3759 - 3830
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 273
- Number
- 12
- Start Page
- 3759
- End Page
- 3830
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/150912
- DOI
- 10.1016/j.jfa.2017.07.011
- ISSN
- 0022-1236
- Abstract
- Let (Xn+1, g(+)) be an (n + 1)-dimensional asymptotically hyperbolic manifold with conformal infinity (M-n, [(h) over cap]). The fractional Yamabe problem addresses to solve P-gamma[g(+), (h) over cap](u) = cu(n+2 gamma/n-2 gamma), u ˃ 0 on M where c is an element of R and P-gamma[g(+) , (h) over cap] is the fractional conformal Laplacian whose principal symbol is the Laplace-Beltrami operator (-Delta)(gamma) on M. In this paper, we construct a metric on the half space X = R-+(n+1), which is conformally equivalent to the unit ball, for which the solution set of the fractional Yamabe equation is non -compact provided that n ˃= 24 for gamma is an element of (0, gamma*) and n ˃= 25 for gamma is an element of [gamma*,1) where gamma* is an element of (0,1) is a certain transition exponent. The value of gamma* turns out to be approximately 0.940197.
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