Duke Mathematical Journal

Asymptotic shape of cusp singularities in curve shortening

S. B. Angenent and J. J. L. Velázquez

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Article information

Source
Duke Math. J. Volume 77, Number 1 (1995), 71-110.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077286147

Digital Object Identifier
doi:10.1215/S0012-7094-95-07704-7

Mathematical Reviews number (MathSciNet)
MR1317628

Zentralblatt MATH identifier
0829.35058

Subjects
Primary: 58E10: Applications to the theory of geodesics (problems in one independent variable)
Secondary: 53A04: Curves in Euclidean space

Citation

Angenent, S. B.; Velázquez, J. J. L. Asymptotic shape of cusp singularities in curve shortening. Duke Math. J. 77 (1995), no. 1, 71--110. doi:10.1215/S0012-7094-95-07704-7. http://projecteuclid.org/euclid.dmj/1077286147.


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References

  • [Alt] S. J. Altschuler, Singularities of the curve shrinking flow for space curves, J. Differential Geom. 34 (1991), no. 2, 491–514.
  • [A] S. B. Angenent, On the formation of singularities in the Curve Shortening Flow, J. Differential Geom. 33 (1991), no. 3, 601–633.
  • [A1] S. Angenent, The zeroset of a solution of a parabolic equation, J. Reine Angew. Math. 390 (1988), 79–96.
  • [Ei] S. D. Eidelman, Parabolic Systems, Translated from the Russian by Scripta Technica, London, North-Holland, Amsterdam, 1969.
  • [FM] A. Friedman and B. McLeod, Blow-up of solutions of nonlinear degenerate parabolic equations, Arch. Rational Mech. Anal. 96 (1986), no. 1, 55–80.
  • [GH] M. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom. 23 (1986), no. 1, 69–96.
  • [Gr] M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. 26 (1987), no. 2, 285–314.
  • [Ma] H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional semi-linear parabolic equation, J. Fac. Sci. Univ. Tokyo, Sect. IA 29 (1982), no. 2, 401–441.
  • [V] J. J. L. Velázquez, Blow-up for semilinear parabolic equations, to appear in Recent Advances in Partial Differential Equations, ed. by M. A. Herrero and E. Zuazua, Masson, 1994.
  • [Wa] P. A. Watterson, Force-free magnetic evolution in the reversed-field pinch, Thesis, Cambridge University, 1985.