Ricci flow on Kähler-Einstein manifolds

X. X. Chen, G. Tian

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

This is the continuation of our earlier article [10]. For any Köhler-Einstein surfaces with positive scalar curvature, if the initial metric has positive bisectional curvature, then we have proved (see [10]) that the Kähler-Ricci flow converges exponentially to a unique Kähler-Einstein metric in the end. This partially answers a long-standing problem in Ricci flow: On a compact Kähler-Einstein manifold, does the Kähler-Ricci flow converge to a Kähler-Einstein metric if the initial metric has positive bisectional curvature? In this article we give a complete affirmative answer to this problem.

Original languageEnglish (US)
Pages (from-to)17-73
Number of pages57
JournalDuke Mathematical Journal
Volume131
Issue number1
DOIs
StatePublished - Jan 1 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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