Inventiones mathematicae

, Volume 96, Issue 1, pp 177–180 | Cite as

The shape of a figure-eight under the curve shortening flow

  • Matthew A. Grayson


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abresch, U., Länger, J.: The normalized curve shortening flow and homothetic solutions. J. Differ. Geom.23, 175–196 (1986)Google Scholar
  2. 2.
    Angenent, S.: The zeroset of a solution of a parabolic equation. PreprintGoogle Scholar
  3. 3.
    Epstein, C., Weinstein, M.: A stable manifold theorem for the curve shortening equation. Commun. Pure Appl. Math.40, 119–139 (1987)Google Scholar
  4. 4.
    Gage, M.: An isoperimetric inequality with application to curve shortening. Duke Math. J.50, 1225–1229 (1983)Google Scholar
  5. 5.
    Gage, M.: Curve shortening makes convex curves circular. Invent. Math.76, 357–364 (1984)Google Scholar
  6. 6.
    Gage, M., Hamilton, R.S.: The heat equation shrinking convex plane curves. J. Differ. Geom.23, 69–96 (1986)Google Scholar
  7. 7.
    Grayson, M.: The heat equation shrinks embedded plane curves to round points. J. Differ. Geom.26, 285–314 (1987)Google Scholar
  8. 8.
    Grayson, M.: Shortening embedded curves. Ann. Math. (to appear)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Matthew A. Grayson
    • 1
  1. 1.Department of MathematicsUniversity of San DiegoLa JollaUSA

Personalised recommendations