### Abstract

These notes give an introduction to the Kähler–Ricci flow. We give an exposition of a number of well-known results including: maximal existence time for the flow, convergence on manifolds with negative and zero first Chern class, and behavior of the flow in the case when the canonical bundle is big and nef. We also discuss the collapsing of the Kähler–Ricci flow on the product of a torus and a Riemann surface of genus greater than one. Finally, we discuss the connection between the flow and the minimal model program with scaling, the behavior of the flow on general Kähler surfaces and some other recent results and conjectures.

Original language | English (US) |
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Title of host publication | An Introduction to the Kahler-Ricci Flow |

Publisher | Springer Verlag |

Pages | 89-188 |

Number of pages | 100 |

ISBN (Print) | 9783319008189 |

DOIs | |

State | Published - Jan 1 2013 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2086 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Song, J., & Weinkove, B. (2013). An Introduction to the Kähler–Ricci Flow. In

*An Introduction to the Kahler-Ricci Flow*(pp. 89-188). (Lecture Notes in Mathematics; Vol. 2086). Springer Verlag. https://doi.org/10.1007/978-3-319-00819-6_3