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On a perimeter-preserving plane curve flow

On a perimeter-preserving plane curve flow The purpose of this paper is to investigate a new type of evolution problem for closed convex plane curves which will preserves the perimeter of the curve but expands the enclosed area and the final limiting curve is a circle in the Hausdorff metric in the plane. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

On a perimeter-preserving plane curve flow

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Publisher
Springer Journals
Copyright
Copyright © 2001 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-001-0009-z
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to investigate a new type of evolution problem for closed convex plane curves which will preserves the perimeter of the curve but expands the enclosed area and the final limiting curve is a circle in the Hausdorff metric in the plane.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Jun 27, 2001

References

  • The normalized curve shortening flow and homothetic solutions
    Abresch, U.; Langer, J.
  • An isoperimetric inequality with applications to curve shortening
    Gage, M. E.
  • Curve shortening makes convex curves circular
    Gage, M. E.
  • The heat equation shrinking convex plane curves
    Gage, M. E.; Hamilton, R. S.
  • The heat equation shrinks embedded plane curve to round points
    Grayson, M.
  • Evolving convex curves
    Andrews, B.
  • Geometric expanding of convex plane curves
    Chow, B.; Tsai, D. H.
  • Geometric expansions of star-shaped curves
    Tsai, D.H.
  • Flow by mean curvature of convex surfaces into spheres
    Huisken, G.
  • Asymptotic behaviour for singularities of the mean curvature flow
    Huisken, G.
  • Mean curvature flow through singularities for surfaces of rotation
    Altschuler, S.; Angenent, S. B.; Giga, Y.
  • Deforming a hypersurface by its Gauss-Kronecker curvature
    Tso, K.
  • The volume preserving mean curvature flow
    Huisken, G.
  • Volume-preserving mean curvature flow of rotationally symmetric surfaces
    Athanassenas, M.
  • A note on the general plane curve flows
    Pan, S. L.
  • A First Course in Differential Geometry
    Hsiung, C. C.
  • Bonnesen-style isoperimetric inequalities
    Osserman, R.