Classification of Limiting Shapes for Isotropic Curve Flows
نویسنده
چکیده
with α 6= 0, and initial condition x(p, 0) = x0(p). This produces a family of curves γt = x(S, t). Here κ is the curvature, and n is the outward-pointing unit normal vector. These equations are particularly natural in that they are isotropic (equivariant under rotations in the plane) and homogeneous (equivariant under dilation of space, if time is also scaled accordingly). The main aim of this paper is to provide a complete description of the behaviour of embedded convex curves moving by equations of the form (1.1). In certain cases this description has already been provided: If α = 1 then Equation (1.1) is the curve-shortening flow, for which the following holds:
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