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math.DG2025
On the planar free elastic flow with small oscillation of curvature
Ben Andrews, Glen Wheeler
The free elastic flow that begins at any closed curve exists for all time. If the initial curve is an -fold covered circle (``-circle'') the solution expands self-similarly.…
math.DG2025
The curve-lengthening flow in inversive geometry
Ben Andrews, Glen Wheeler
We consider an invariant gradient flow for the invariant length functional for co-compact curves in inversive geometry, and prove that solutions exist for all time and converge to…