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I was given the PDE $C_t = (L/2\pi - 1/k)N(p,t) $ and $C(p,0) = C_0(p)$ where $k$ = curvature of the evolving curve, and $C(p,t)$ is the family of closed planar curves.

I was asked to show that this PDE does indeed evolve a planar curve to a circle while preserving its length, but I'm not sure how to show that $L'(t) = 0$ (Length preservation) or to show how it evolves a curve to a curve, because I'm rather weak in calculus. Please help.

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    Did you mean $C(p,t)$ for $N(p,t)$?2012-03-06
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    @Ilya: I don't think so. The $N(p,t)$ probably refers to the normal vector at the point $C(p,t)$.2012-03-07

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