Research profile

Robb McDonald

Works on curve shortening and self-shrinkers & translators.

NP-RC-615820

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2021

math.DGWider flowsv3arXiv:2103.06069

The fundamental solutions of the curve shortening problem via the Schwarz function

Robb McDonald

Curve shortening in the -plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy , where is the Schwarz function of the curve. This equation is shown to have a parametric solution from which the known explicit solutions for curve shortening flow; the circle, grim reaper, paperclip and hairclip, can be recovered.

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