The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow
Source abstract
Abstract
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation of a shrinking figure eight curve.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Geometry and complex manifolds
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References (26)
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