Remarks on Kahler Ricci Flow

Details Remarks on Kahler Ricci Flow Remarks on Kahler Ricci Flow

2008-09-23

arxiv.org/abs/0809.3963v2

Mathematics

Differential Geometry

We note an overlap with the paper of Rubinstein [Ru1]. We add more reference

Scientific paper

We study some estimates along the Kahler Ricci flow on Fano manifolds. Using these estimates, we show the convergence of Kahler Ricci flow directly if the $\alpha$-invariant of the canonical class is greater than $\frac{n}{n+1}$. Applying these convergence theorems, we can give a flow proof of Calabi conjecture on such Fano manifolds. In particular, the existence of Kahler Einstein metrics on a lot of Fano surfaces can be proved by flow method. Note that this geometric conclusion (based on the same assumption) was established earlier via elliptic method by G. Tian. However, a new proof based on Kahler Ricci flow should be still interesting in its own right.

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