An Introduction to the Kähler–Ricci Flow

Jian Song*, Ben Weinkove

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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 languageEnglish (US)
Title of host publicationAn Introduction to the Kahler-Ricci Flow
PublisherSpringer Verlag
Pages89-188
Number of pages100
ISBN (Print)9783319008189
DOIs
StatePublished - Jan 1 2013

Publication series

NameLecture Notes in Mathematics
Volume2086
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