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BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)

Published online by Cambridge University Press:  10 April 2008

Natasa Sesum  and
Gang Tian
Natasa Sesum
Affiliation:
Department of Mathematics, Columbia University, Room 509, MC 4406, 2990 Broadway, New York, NY 10027, USA (natasas@cpw.math.columbia.edu)
Gang Tian
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA (tian@math.princeton.edu)
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Abstract

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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.

Keywords

scalar curvaturediameterKähler Ricci flowPrimary 53C44
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 3 , July 2008 , pp. 575 - 587
Copyright
2008 Cambridge University Press