Journal of Differential Geometry

The heat equation shrinking convex plane curves

M. Gage and R. S. Hamilton

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Article information

J. Differential Geom., Volume 23, Number 1 (1986), 69-96.

First available in Project Euclid: 26 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A04: Curves in Euclidean space
Secondary: 35K05: Heat equation 52A40: Inequalities and extremum problems 58E99: None of the above, but in this section 58G11


Gage, M.; Hamilton, R. S. The heat equation shrinking convex plane curves. J. Differential Geom. 23 (1986), no. 1, 69--96. doi:10.4310/jdg/1214439902.

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  • [1] M. Gage, An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50 (1983) 1225-1229.
  • [2] M. Gage, Curve shortening makes convex curves circular, Invent. Math. 76 (1984) 357-364.
  • [3] H. Guggenheimer, Differential geometry, Dover Publications, 1977.
  • [4] R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc.
  • [5] R. S. Hamilton, Three manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982) 255-306.
  • [6] Gerhard Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
  • [7] D. S. Mitrinovic, Analytic inequalities, Springer, 1970.
  • [8] R. Osserman, Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979).
  • [9] F. Warner, Foundations of differentiate manifolds and Lie groups, Scott, Foresman and Co., 1971.