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Convergence of Kähler-Ricci flow on lower-dimensional algebraic manifolds of general type. (English) Zbl 1404.53085

Summary: In this paper, we prove that the \(L^4\)-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold \(M\) of general type and with dimension \(n\leq 3\), any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of \(M\) in the Cheeger-Gromov topology.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
32Q15 Kähler manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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