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

Dimitra Antonopoulou; Georgia Karali

doi:10.3934/nhm.2013.8.9

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2013, Volume 8, Issue 1: 9-22. Doi: 10.3934/nhm.2013.8.9

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

Dimitra Antonopoulou^1, and
Georgia Karali^1,

1.
Department of Applied Mathematics, University of Crete, 714 09 Heraklion

Received: September 2011

Published: March 2013

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Abstract

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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Mathematics Subject Classification: Primary: 35; Secondary: 37.

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References

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