A nonlinear partial differential equation for the volume preserving mean curvature flow

@article{Antonopoulou2013ANP,
  title={A nonlinear partial differential equation for the volume preserving mean curvature flow},
  author={D. C. Antonopoulou and Georgia D. Karali},
  journal={NHM},
  year={2013},
  volume={8},
  pages={9-22}
}
We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this flow, to observe that they become convex very fast. 

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References

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Showing 1-10 of 12 references

The Heat Equation shrinks embedded plane curves to round points

  • M. A. Grayson
  • J. Differential Geom., 26
  • 1987
Highly Influential
4 Excerpts

Stability of spheres under volume preserving mean curvature flow

  • D. C. Antonopoulou, G. D. Karali, I. M. Sigal
  • Dynamics of PDE, 7
  • 2010
5 Excerpts

The normalized mean curvature flow for a small bubble in a Riemannian manifold

  • N. D. Alikakos, A. Freire
  • J. Differential Geom., 64
  • 2003
2 Excerpts

Partial Differential Operators of Elliptic Type,

  • N. Shimakura
  • Translations of Mathematical Monographs,
  • 1992
1 Excerpt

Shimakura “ Partial Differential Operators of Elliptic Type

  • N.
  • Differential Geometry
  • 1991

On an area-preserving evolution equation for plane curves

  • M. Gage
  • Nonlinear Problems in Geometry, D. M. DeTurck…
  • 1986
2 Excerpts

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