Skip to main content
Log in

Uniqueness for Ricci flow with unbounded curvature in dimension 2

  • Original Paper
  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We consider the uniqueness of Ricci flow with the initial curvature bounded from above, but not necessarily bounded from below, on a 2-dimensional complete noncompact manifold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Calabi E.: An extension of E. Hopf’s maximum principle with an application to geometry. Duke Math. J. 25, 285–303 (1965)

    MathSciNet  Google Scholar 

  2. Chavel I.: Eigenvalues in Riemannian Geometry. Acadamic press Inc., New York (1984)

    MATH  Google Scholar 

  3. Chen, Q., Yan, Y.: Ricci flow on surfaces with unbounded initial metric, preprint

  4. Chen B., Zhu X.: Uniqueness of the Ricci flow on complete noncompact manifolds. J. Differ. Geom. 74(1), 119–154 (2006)

    MATH  MathSciNet  Google Scholar 

  5. Chow B., Lu P., Ni L.: Hamilton’s Ricci Flow. American Mathematical Society, Providence (2005)

    Google Scholar 

  6. DeTurck D.M.: Deforming the Metrics in the Direction of Ricci Tensors (Improved Version), in Collected Papers on Ricci Flow. International press, Somerville (2003)

    Google Scholar 

  7. Dodziuk J.: Maximum principle for parabolic inequalities and the heat flow on open manifolds. Univ. Math. J. 32, 703–716 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hamilton R.S.: Three-manifolds with positive Ricci curvature. J. Differ. Geom. 17, 255–306 (1982)

    MATH  MathSciNet  Google Scholar 

  9. Hsu, S.: Uniqueness of solutions of Ricci flow on complete noncompact manifolds. ArXiv:math.DG/ 0704.3468v2

  10. Simon M: Ricci flow of almost non-negatively curved three manifolds. J. Reine Angew. Math. 630, 177–217 (2009)

    MATH  MathSciNet  Google Scholar 

  11. Simon, M.: Ricci flow of non-collapsed 3-manifolds with Ricci curvature is bounded form below. ArXiv:math.DG/0903.2142

  12. Topping, P.: Ricci flow compactness via pseudolocality and flows with incomplete initial metrics. http://www.warwick.ac.uk/~maseq

  13. Yazhe C.: 2-Order Parabolic Type Partial Differential Equation. Peiking university press, Beijing (2003)

    Google Scholar 

  14. Yau S.-T., Schoen R.: Lectures on Differential Geometry. International Press, Boston (1994)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qing Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Q., Yan, Y. Uniqueness for Ricci flow with unbounded curvature in dimension 2. Ann Glob Anal Geom 38, 293–303 (2010). https://doi.org/10.1007/s10455-010-9214-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10455-010-9214-4

Keywords

Navigation