Motion of Hypersurfaces by Gauss Curvature

  title={Motion of Hypersurfaces by Gauss Curvature},
  author={B. Andrews},
We consider n-dimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature. We prove that hypersurfaces contract to points in finite time, and for α ∈ (1/(n + 2], 1/n] we also prove that in the limit the solutions evolve purely by homothetic contraction to the final point. We prove existence and uniqueness of solutions for non-smooth initial hypersurfaces, and develop upper and lower bounds on the speed and the curvature… CONTINUE READING

From This Paper

Topics from this paper.
23 Citations
26 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 26 references

Second order parabolic differential equations

  • G. M. Lieberman
  • World Scientific, Singapore,
  • 1996

Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birk-häuser

  • A. Lunardi
  • 1995

Contraction of convex hypersurfaces in Euclidean space, Calc

  • B. Andrews
  • Var. & P.D.E.,
  • 1994

Singularities and self-intersections of curves evolving on surfaces

  • J. Oaks
  • Indiana Univ. Math. J.,
  • 1994

Worn stones with flat sides, in ‘A tribute to Ilya Bakelman

  • R. Hamilton
  • (College Station,
  • 1994

Axioms and fundamental equations of image processing

  • P. L. Lions
  • Arch . Rat . Mech . Anal .
  • 1993

Axioms and fundamental equations of image processing, Arch

  • AGLM L. Alvarez, F. Guichard, P. L. Lions, J. M. Morel
  • Rat. Mech. Anal.,
  • 1993

Similar Papers

Loading similar papers…