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math.AP2024★ 3 cited
The free elastic flow for closed planar curves
Tatsuya Miura, Glen Wheeler
The free elastic flow is the -gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows…
math.AP2024★ 2 cited
Uniqueness and minimality of Euler's elastica with monotone curvature
Tatsuya Miura, Glen Wheeler
For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped…