Skip to main content
Log in

Existence of selfsimilar shrinking curves for anisotropic curvature flow equations

  • Published:
Calculus of Variations and Partial Differential Equations Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. Angenent: On the Formation of Singularities in the Curve Shortening Flow. J. Differ. Geom.33 (1991) 601–633.

    Google Scholar 

  2. A. Ambrosetti, V. Coti Zelati: Periodic Solutions of Singular Lagrangian Systems. Birkhäuser, Zürich (1993).

  3. U. Abresch, J. Langer: The Normalized Curve Shortening Flow and Homothetic Solutions. J. Differ. Geom.23 (1986) 175–196.

    Google Scholar 

  4. V. Coti Zelati: Dynamical Systems with Effektive-like Potentials. Nonlin. Anal. Appl.12 (1988) 209–222.

    Google Scholar 

  5. K. Deimling: Nonlinear Functional Analysis, Springer, Heidelberg Berlin New York (1985).

    Google Scholar 

  6. C. Dohmen, Y. Giga: Selfsimilar Shrinking Curves for Anisotropie Curvature Flow Equations. Proc. Japan Acad. Ser. A70 (1994) 252–255.

    Google Scholar 

  7. C. Epstein, M. Weinstein: A Stable Manifold Theorem for the Curve Shortening Equation. Comm. Pure Appl. Math.40 (1987) 119–139.

    Google Scholar 

  8. M. Gage: An Isoperimetric Inequality With Application to Curve Shortening. Duke M. J.50 (1983) 1225–1229.

    Google Scholar 

  9. M. Gage: Curve Shortening Makes Convex Curves Circular. Invent. Math.76 (1984) 357–364.

    Google Scholar 

  10. M. Gage: Evolving Plane Curves by Curvature in Relative Geometries. Duke M. J.72 (1993) 441–466.

    Google Scholar 

  11. M. Gage, R.S. Hamilton: The Heat Equation Shrinking Convex Plane Curves. J. Differ. Geom.23 (1986) 69–96.

    Google Scholar 

  12. M. Gage, Yi Li: Evolving Plane Curves by Curvature in Relative Geometries II. Preprint No. 19 (1992) University of Rochester.

  13. M. Grayson: The Heat Equation Shrinks Embedded Plane Curves to Points. J. Differ. Geom.26 (1987) 285–314.

    Google Scholar 

  14. M.E. Gurtin: Thermodynamics of Evolving Phase Boundaries in the Plane. Clarendon Press, Oxford (1993).

    Google Scholar 

  15. L. Nirenberg: Topics in Nonlinear Functional Analysis. Lecture Notes 1973/74, Courant Inst. of Math. Sciences.

  16. S. Solimini: On Forced Dynamical Systems With a Singularity of Repulsive Type. Nonlin. Anal. Appl.14 (1990) 485–500.

    Google Scholar 

  17. H.M. Soner: Motion of a Set By the Curvature of Its Boundary. J. Differ. Eq.101 (1993) 313–392.

    Google Scholar 

  18. S. Terracini: Remarks on Periodic Orbits of Dynamical Systems With Repulsive Singularity. J. Funct. Anal.111 (1993) 213–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dohmen, C., Giga, Y. & Mizoguchi, N. Existence of selfsimilar shrinking curves for anisotropic curvature flow equations. Calc. Var 4, 103–119 (1996). https://doi.org/10.1007/BF01189949

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01189949

Keywords

Navigation