TL;DR
This paper demonstrates the existence of various complex geometric solutions, called jellyfish, for different flow equations in differential geometry, highlighting the richness of these flows.
Contribution
It proves the existence of infinitely many distinct solutions, called jellyfish, for elastic flow, curve diffusion flow, and ideal flow, expanding understanding of these geometric flows.
Findings
Existence of infinitely many homothetic expanders for elastic flow.
Existence of epicyclic shrinkers for curve diffusion flow.
Existence of epicyclic expanders for ideal flow.
Abstract
We show the existence of infinitely many geometrically distinct homothetic expanders (jellyfish) for the elastic flow, epicyclic shrinkers for the curve diffusion flow, and epicyclic expanders for the ideal flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology