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Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds.
- Source :
-
Communications in Contemporary Mathematics . May2019, Vol. 21 Issue 3, pN.PAG-N.PAG. 51p. - Publication Year :
- 2019
-
Abstract
- We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension n ≥ 3. We prove the existence of such conformal metrics in the cases of n = 6 , 7 or the manifold is spin and some other remaining ones left by Escobar. Furthermore, in the positive Yamabe constant case, by normalizing the scalar curvature to be 1 , there exists a sequence of conformal metrics such that their constant boundary mean curvatures go to + ∞. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 21
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 136242041
- Full Text :
- https://doi.org/10.1142/S0219199718500219