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An Introduction to the Kähler-Ricci Flow pp 89–188Cite as

An Introduction to the Kähler–Ricci Flow

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2086))

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.

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Acknowledgements

Jian Song is supported in by an NSF CAREER grant DMS-08-47524 and a Sloan Research Fellowship. Ben Weinkove is supported by the NSF grants DMS-08-48193 and DMS-11-05373.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Jian Song

  2. Department of Mathematics, University of California San Diego, La Jolla, CA, 92093, USA

    Ben Weinkove

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  1. Institut de Mathématiques de Jussieu, CNRS-Université Pierre et Marie Curie, Paris, France

    Sebastien Boucksom

  2. Institut Fourier and Institut Universitaire de France, Université Joseph Fourier, Saint-Martin d'Hères, France

    Philippe Eyssidieux

  3. Institut de Mathématiques de Toulouse and Institut Universitaire de France, Université Paul Sabatier, Toulouse, France

    Vincent Guedj

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Song, J., Weinkove, B. (2013). An Introduction to the Kähler–Ricci Flow. In: Boucksom, S., Eyssidieux, P., Guedj, V. (eds) An Introduction to the Kähler-Ricci Flow. Lecture Notes in Mathematics, vol 2086. Springer, Cham. https://doi.org/10.1007/978-3-319-00819-6_3

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