Advertisement

The Mathematical Intelligencer

, Volume 29, Issue 4, pp 34–43 | Cite as

Ricci Flow and the Poincaré Conjecture

  • Siddhartha GadgilEmail author
  • Harish Seshadri
Article
  • 186 Downloads

Keywords

Manifold Riemannian Manifold Scalar Curvature Sectional Curvature Mathematical Intelligencer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. T. Anderson, Geometrization of 3-manifolds via the Ricci flow,Notices Arner. Math. Soc. 51 (2004), no. 2, 184–193.zbMATHGoogle Scholar
  2. [2]
    H.-D. Cao, X.-P. Zhu, A Complete Proof of the Poincaré and Geometrization Conjectures—Application of the Hamilton-Perel-man Theory of the Ricci Flow,Asian Journal of Mathematics 10 (2006), no. 2, 185–492.CrossRefMathSciNetGoogle Scholar
  3. [3]
    H.-D. Cao, X.-P. Zhu, Erratum to “A Complete Proof of the Poincare and Geometrization Conjectures—Application of the Hamilton-Perelman Theory of the Ricci Flow”,Asian Journal of Mathematics 10 (2006), no. 4, 663.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    T. H. Colding, W. P. Minicozzi: Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman,Journal Amer. Math. Soc. 18 (2005), no. 3, 561–569.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    R. S. Hamilton, Three-manifolds with positive Ricci curvature,J. Differential Geom. 17 (1982), no. 2, 255–306.zbMATHMathSciNetGoogle Scholar
  6. [6]
    R. S. Hamilton, The Formation of Singularities in the Ricci Flow,Surveys in Differential Geometry, Vol. II (Cambridge, MA, 1993), 7–136, Intemat. Press, Cambridge, MA, 1995.Google Scholar
  7. [7]
    B. Kleiner, J. Lott, Notes on Perelman’s papers, math.DG/0605667.Google Scholar
  8. [8]
    J. Milnor, Towards the Poincaré conjecture and the classification of 3-manifolds,Notices Amer. Math. Soc. 50(2003), no. 10, 1226–1233.zbMATHMathSciNetGoogle Scholar
  9. [9]
    J. Morgan, G. Tian, Ricci flow and the Poincaré conjecture, math.DG/0605667.Google Scholar
  10. [10]
    G. Perelman, The entropy formula for the Ricci flow and its geometric application, math.DG/0211159.Google Scholar
  11. [11]
    G. Perelman, Ricci flow with surgery on three-manifolds, math.DG/0211159.Google Scholar
  12. [12]
    G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, math.DG/0211159.Google Scholar
  13. [13]
    W. P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry,Bull. Amer. Math. Soc. (N.S.) 6 (1982), no.3, 357–381.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    P. Topping, Lectures on the Ricci Flow, www.maths.warwick.ac.uk/topping/RFnotes.htmlGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc 2007

Authors and Affiliations

  1. 1.Department of MathematicsImdian Institute of ScienceBangaloreIndia

Personalised recommendations