87
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Ricci flows with bursts of unbounded curvature

&
Pages 854-876 | Received 29 May 2015, Accepted 12 Dec 2015, Published online: 02 Jun 2016

References

  • Bol, G. (1941). Isoperimetrische Ungleichungen für Bereiche auf Flächen. Jahresbericht der Deutschen Mathematiker-Vereinigung 51:219–257.
  • Chen, B.-L. (2009). Strong uniqueness of the Ricci flow. J. Differ. Geom. 82:363–382.
  • Chow, B. (1991). The Ricci flow on the 2-sphere. J. Differ. Geom. 33:325–334.
  • Cabezas-Rivas, E., Wilking, B. (2015). How to produce a Ricci Flow via Cheeger-Gromoll exhaustion. J. Eur. Math. Soc. 17:3153–3194.
  • Giesen, G., Topping, P.M. (2011). Existence of Ricci flows of incomplete surfaces. Comm. Part. Differ. Equ. 36:1860–1880.
  • Giesen, G., Topping, P.M. (2013). Ricci flows with unbounded curvature. Mathematische Zeitschrift 273:449–460.
  • Hamilton, R. S. (1982). Three-manifolds with positive Ricci curvature. J. Differ. Geom. 17:255–306.
  • Hamilton, R. S. (1988). The Ricci flow on surfaces. In: Isenberg, J.A., ed., Mathematics and General Relativity (California: Santa Cruz, 1986). Contemporary Mathematics, vol. 71. Providence, RI: American Mathematical Society, pp. 237–262.
  • Perelman, G. The entropy formula for the Ricci flow and its geometric applications. arXiv:math/0211159, 11 November 2002.
  • Shi, W.-X. (1989). Deforming the metric on complete Riemannian manifolds. J. Differ. Geom. 30:223–301.
  • Topping, P. (1998). Mean curvature flow and geometric inequalities. J. Reine und Angewandte Mathematik 503:47–61.
  • Topping, P. (1999). The isoperimetric inequality on a surface. Manuscripta Mathematica 100:23–23.
  • Topping, P. (2006). Lectures on the Ricci Flow. London Mathematical Society Lecture Note Series, No. 325. Cambridge: Cambridge University Press.
  • Topping, P. (2010). Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics. J. Eur. Math. Soc. 12:1429–1451.
  • Topping, P. M. (2012). Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities. Int. Math. Res. Not. 2012:2356–2376.
  • Topping, P. M. (2014). Remarks on Hamilton's compactness theorem for Ricci flow. J. Reine und Angewandte Mathematik 692:173–191.
  • Topping, P. M. (2015). Uniqueness of instantaneously complete Ricci flows. Geometry and Topology 19:1477–1492.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.