On the existence of extremal metrics for $L^2$-norm of scalar curvature on closed 3-manifolds
Chang, Shu-Cheng ; Wu, Jin-Tong
J. Math. Kyoto Univ., Tome 39 (1999) no. 4, p. 435-454 / Harvested from Project Euclid
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In this paper, based on Bochner formula, mass decay estimates and elliptic Moser iteration, we show the global existence and asymptotic convergence of a subsequence of solutions of Calabi flow on some closed 3-manifolds, and then the existence of extermal metrics of $L^{2}$-norm of scalar curvature functional on a fixed conformal class is claimed. In particular, we may re-solve part of the Yamabe conjecture on closed 3-manifolds.
Publié le : 1999-05-15
Classification:  53C44,  53C21,  58E11 
@article{1250517863,
     author = {Chang, Shu-Cheng and Wu, Jin-Tong},
     title = {On the existence of extremal metrics for $L^2$-norm of scalar curvature on closed 3-manifolds},
     journal = {J. Math. Kyoto Univ.},
     volume = {39},
     number = {4},
     year = {1999},
     pages = { 435-454},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250517863}
}

Chang, Shu-Cheng; Wu, Jin-Tong. On the existence of extremal metrics for $L^2$-norm of scalar curvature on closed 3-manifolds. J. Math. Kyoto Univ., Tome 39 (1999) no. 4, pp.  435-454. http://gdmltest.u-ga.fr/item/1250517863/