Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-20T10:05:13.878Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Gang Tian
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)