Bounding scalar curvature for global solutions of the Kahler-Ricci flow

Details Bounding scalar curvature for global solutions of the Kahler-Ricci flow Bounding scalar curvature for global solutions of the Kahler-Ricci flow

2011-11-24

arxiv.org/abs/1111.5681v1

Mathematics

Differential Geometry

12 pages

Scientific paper

We show that the scalar curvature is uniformly bounded for the normalized Kahler-Ricci flow on a Kahler manifold with semi-ample canonical bundle. In particular, the normalized Kahler-Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kahler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.

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