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- Title
Conformal scalar curvature equation on Sn: Functions with two close critical points (Twin Pseudo-Peaks).
- Authors
Leung, Man Chun; Zhou, Feng
- Abstract
By using the Lyapunov–Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on S n ( n ≥ 3 ) when the prescribed function (after being projected to I R n ) has two close critical points, which have the same value (positive), equal “flatness” (“twin”; flatness < n − 2 ), and exhibit maximal behavior in certain directions (“pseudo-peaks”). The proof relies on a balance between the two main contributions to the reduced functional — one from the critical points and the other from the interaction of the two bubbles.
- Subjects
CRITICAL point (Thermodynamics); SOBOLEV spaces; LYAPUNOV-Schmidt equation; MATHEMATICAL functions; MATHEMATICAL proofs
- Publication
Communications in Contemporary Mathematics, 2018, Vol 20, Issue 5, pN.PAG
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199717500511