Stability on Kähler-Ricci flow, I

Details Stability on Kähler-Ricci flow, I Stability on Kähler-Ricci flow, I

2009-08-11

arxiv.org/abs/0908.1488v1

Mathematics

Differential Geometry

27 pages

Scientific paper

In this paper, we prove that K\"ahler-Ricci flow converges to a K\"ahler-Einstein metric (or a K\"ahler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial K\"ahler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a compact K\"ahler manifold with $c_1(M)>0$ admits a K\"ahler Einstein metric $g_{KE}$ (or a K\"ahler-Ricci soliton $g_{KS}$). The result improves Main Theorem in [TZ3] in the sense of stability of K\"ahler-Ricci flow.

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