Monotonicity of critical points on planar curves evolving under curvature-driven flows
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چکیده
We consider the shrinking of a smooth, closed convex planar curve with inward normal speed v given as v = v(κ) a function of the curvature κ. Grayson proved in 1987 that if v = κ then the number N(t) of spatial critical points (extremal points of a polar distance function measured from a fixed origin) is monotonically decreasing. Here we generalize this result by showing that for the monotonic decrease of N(t) it is sufficient that ∂v ∂κ > 0.
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تاریخ انتشار 2014