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math.DG2023★ 4 cited
General rigidity principles for stable and minimal elastic curves
Tatsuya Miura, Kensuke Yoshizawa
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers…
math.DG2022★ 4 cited
Pinned planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Building on our previous work, we classify all planar -elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. A…
math.DG2021
The critical points of the elastic energy among curves pinned at endpoints
Kensuke Yoshizawa
In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical…