Journal of Differential Geometry

Asymptotic behavior for singularities of the mean curvature flow

Gerhard Huisken

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J. Differential Geom., Volume 31, Number 1 (1990), 285-299.

First available in Project Euclid: 26 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 35B99: None of the above, but in this section 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov) 58G11


Huisken, Gerhard. Asymptotic behavior for singularities of the mean curvature flow. J. Differential Geom. 31 (1990), no. 1, 285--299. doi:10.4310/jdg/1214444099.

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  • [1] U. Abresch and J. Langer, The normalized curveshortening flow and homothetic solutions, J. Differential Geometry 23 (1986) 175-196.
  • [2] M. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geometry 23 (1986) 69-96.
  • [3] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985) 297-319.
  • [4] Y. Giga and R. V. Kohn, Characterizing blow-up using similarity variables, preprint (to appear in Indiana Univ. Math. J.).
  • [5] M. A. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geometry 26 (1987) 285-314.
  • [6] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982) 255-306.
  • [7] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
  • [8] J. Langer, A compactness theorem for surfaces with Lp-bounded second fundamental form, Math. Ann. 270 (1985) 223-234.
  • [9] M. Struwe, On the evolution of harmonic maps in high dimensions, J. Differential Geometry 28 (1988) 485-502.