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.