Singularity Models for the Ricci Flow: An Introductory Survey

  • Dan Knopf
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 59)


At the time this article is being written (May 2003) much of the mathematical world is waiting with intense interest to see the results of Grisha Perelman’s effort [22>, 23] to resolve William Thurston’s Geometrization Conjecture [28] for closed 3-manifolds by completing the program [16] begun by Richard Hamilton. It is still too early to give an accurate and fair assessment of the full impact of Perelman’s work. But in order to aid the many mathematicians who may be inspired by that work to look more closely at the Ricci flow, this does seem like an appropriate time to write a brief and purely expository introduction to the topic, intended for the non-expert. Readers desiring more information are encouraged to read the more advanced survey articles [6] and [7], as well as to consult Hamilton’s and Perelman’s original papers.


Riemannian Manifold Sectional Curvature Singularity Model Ricci Soliton Ricci Flow 
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© Springer Basel AG 2004

Authors and Affiliations

  • Dan Knopf
    • 1
  1. 1.The University of IowaUSA

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