New results and problems on Kähler-Ricci flow

Gang Tian

Research output: Chapter in Book/Report/Conference proceedingChapter

26 Scopus citations

Abstract

In this paper, I give a brief tour on a program of studying the Kähler-Ricci flow with surgery and its interaction with the classification of projective manifolds. The Kähler-Ricci flow may develops singularity at finite time. It is important to understand how to extend the Kähler-Ricci flow across the singular time, that is, construct solution of the Kähler-Ricci flow with surgery. The first task of this paper is to describe a procedure of constructing global solutions for the Kähler-Ricci flow with surgery. This procedure is rather canonical. I will discuss properties of such solutions with surgery and their geometric implications. I will also discuss their asymptotic limits at time infinity. The results discussed here were mainly from my joint works with Z. Zhang, J. Song et al. Some open problems will be also discussed. The paper is mostly expository.

Original languageEnglish (US)
Title of host publicationDifferential Geometry, Mathematical Physics, Mathematics and Society Part 2
Pages71-92
Number of pages22
Edition322
StatePublished - Dec 1 2008

Publication series

NameAsterisque
Number322
ISSN (Print)0303-1179

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Kähler-Einstein metrics
  • Kähler-Ricci flow

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  • Cite this

    Tian, G. (2008). New results and problems on Kähler-Ricci flow. In Differential Geometry, Mathematical Physics, Mathematics and Society Part 2 (322 ed., pp. 71-92). (Asterisque; No. 322).