Ricci Flow and the Poincaré Conjecture

  • Steven G. Krantz
  • Harold R. Parks


Jules Henri Poincaré (1854–1912) was one of the great geniuses of nineteenth and twentieth-century mathematics. Born into a distinguished family of academicians and public servants, he showed early talent in mathematics and science. Indeed, the entire country of France watched in awe as Poincaré developed from a child prodigy to a major leader in mathematics and physics.


Clay Entropy Manifold Rubber Expense 

References and Further Reading

  1. [CZ 06]
    Cao, H.-D., Zhu, X.-P.: A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian Journal of Mathematics 10, 165–498 (2006)CrossRefMATHMathSciNetGoogle Scholar
  2. [KL 08]
    Kleiner, B., Lott, J.: Notes on Perelman’s papers. Geometry & Topology 12, 2587-2855 (2008)CrossRefMATHMathSciNetGoogle Scholar
  3. [Kuh 70]
    Kuhn, T.S.: The Structure of Scientific Revolutions, 2nd edn. University of Chicago Press, Chicago (1970)Google Scholar
  4. [MT 07]
    Morgan, J., Tian, G.: Ricci flow and the Poincaré conjecture. In: Clay Mathematics Monographs, American Mathematical Society, Providence (2007)Google Scholar
  5. [MT 08]
    Morgan, J., Tian, G.: Completion of the proof of the geometrization conjecture. arXiv:0809.4040v1[math.DG]Google Scholar
  6. [Per(a)]
    Perelman, G.: The entropy formula for the Ricci flow and its geometric applications (2008). arXiv:math.DG/0211159v1Google Scholar
  7. [Per(b)]
    Perelman, G.: Ricci flow with surgery on three-manifolds (2008). arXiv:math.DG/0303109v1Google Scholar
  8. [Per(c)]
    Perelman, G.: Finite extinction time for the solutions to the Ricci flow on certain three-manifolds (2008). arXiv:math.DG/ 0307245v1Google Scholar
  9. [Poi 04]
    Poincaré, H.: Cinquième complément á l’analysus situs. In: Œuvres de Poincaré, pp. 435–498. Gauthier-Villars, Tome. VI, Paris (1953). Originally published in Rendiconti de Circolo Matematica di Palermo, 18 (1904), 45–110Google Scholar
  10. [Strz 06]
    Strzelecki, P.: The Poincaré conjecture? American Mathematical Monthly 113, 75–78 (2006)CrossRefMATHMathSciNetGoogle Scholar
  11. [Thu 80]
    Thurston, W.P.: The Geometry and Topology of Three- Manifolds. Notes. Princeton University, Princeton, NJ (1980)Google Scholar
  12. [Thu 82]
    Thurston, W.P.: 3-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bulletin of the American Mathematical Society 6, 357–381 (1982)CrossRefMATHMathSciNetGoogle Scholar
  13. [Thu 94]
    Thurston, W.P.: On proof and progress in mathematics. Bulletin of the American Mathematical Society 30, 161–177 (1994)CrossRefMATHMathSciNetGoogle Scholar
  14. [Thu 97]
    Thurston, W.P.: 3-Dimensional Geometry and Topology, vol. 1. Princeton University Press, Princeton (1997)Google Scholar
  15. [Wil 42]
    Wilson, L.: The Academic Man, A Study in the Sociology of a Profession. Oxford University Press, London (1942)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Steven G. Krantz
    • 1
  • Harold R. Parks
    • 2
  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvalisUSA

Personalised recommendations