Abstract
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.
Citation
Shu-Cheng Chang. Jin-Tong Wu. "On the existence of extremal metrics for $L^2$-norm of scalar curvature on closed 3-manifolds." J. Math. Kyoto Univ. 39 (3) 435 - 454, 1999. https://doi.org/10.1215/kjm/1250517863
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