Yu, Zheng The negative gradient flow for the \(L^2\)-integral of Ricci curvature. (English) Zbl 1054.53080 Manuscr. Math. 111, No. 2, 163-186 (2003). The author introduces the negative gradient flow for the \(L^2\)-integral of the Ricci curvature and proves the short time existence. In dimension 3, the author also proves that (1) if the maximal time interval \([0, T)\) of existence of solution is infinite, the solution \(g(t)\) converges to a flat metric, and (2) if the interval is finite, then as \(t\rightarrow T\), either the curvature is unbounded or the manifold collapses. Reviewer: Mingliang Cai (Coral Gables) Cited in 3 Documents MSC: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:negative gradient flow; short time existence; time interval; flat metric PDFBibTeX XMLCite \textit{Z. Yu}, Manuscr. Math. 111, No. 2, 163--186 (2003; Zbl 1054.53080) Full Text: DOI