Evolution of spoon-shaped networks

Date(s) : 26/05/2015   iCal
11 h 00 min - 12 h 00 min

After defining a regular planar network of curves, we study its motion by curvature. In particular, we focus on two model cases: we consider a regular embedded network composed by three curves with fixed endpoints (triod) and a regular embedded network composed by two curves, one of which is closed (spoon), and we study their evolution by curvature. The first one converges to the Steiner minimal connection between the three endpoints, if the lengths of the three curves stay far from zero. In the second case we show that the maximal existence time depends only on the area enclosed in the initial loop. Moreover, the closed curve becomes eventually convex and then shrinks homotetically to a point, approaching the shape of a Brakke spoon.



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