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Curve flows on ruled surfaces. (English) Zbl 1297.53045
The authors study different flows of curves on surfaces. They give different implementations of the flows and compare them. In particular they give an implementation of the Crank-Nicolson method and examples which show an interesting topological phenomenon: The curvature radius flow respects the winding number of a plane curve while the curvature flow does not.
They then prove that, when the surface is a ruled surface, under the Gaussian flow in the direction of the ruling a curve converges to the striction curve (locus of maximal Gaussian curvature) and conjecture that under the geodesic flow the curve converges to a closed geodesic.

MSC:
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
37E35 Flows on surfaces
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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