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kähler ricci flow

Journal of the Institute of Mathematics of Jussieu (1)

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BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)
Natasa Sesum, Gang Tian
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 7 / Issue 3 / July 2008

Published online by Cambridge University Press:

10 April 2008, pp. 575-587

Print publication:

July 2008
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In this short note we present a result of Perelman with detailed proof. The result states that if $g(t)$ is the Kähler Ricci flow on a compact, Kähler manifold $M$ with $c_1(M)>0$, the scalar curvature and diameter of $(M,g(t))$ stay uniformly bounded along the flow, for $t\in[0,\infty)$. We learned about this result and its proof from Grigori Perelman when he was visiting MIT in the spring of 2003. This may be helpful to people studying the Kähler Ricci flow.