Classification and stability of penalized pinned elasticae
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908650756374528 |
|---|---|
| author | Müller, Marius Yoshizawa, Kensuke |
| author_facet | Müller, Marius Yoshizawa, Kensuke |
| contents | This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a special penalization parameter $\hatλ\simeq 0.70107$. Stability of all the critical points is also investigated, and again the threshold $\hatλ$ plays a decisive role. In addition, our explicit parametrization is applied to compare the energy of critical points, leading to uniqueness of minimal nontrivial critical points. As an application we obtain eventual embeddedness of elastic flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification and stability of penalized pinned elasticae Müller, Marius Yoshizawa, Kensuke Analysis of PDEs Differential Geometry Primary: 53A04, Secondary: 49Q10, 53E40 This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a special penalization parameter $\hatλ\simeq 0.70107$. Stability of all the critical points is also investigated, and again the threshold $\hatλ$ plays a decisive role. In addition, our explicit parametrization is applied to compare the energy of critical points, leading to uniqueness of minimal nontrivial critical points. As an application we obtain eventual embeddedness of elastic flows. |
| title | Classification and stability of penalized pinned elasticae |
| topic | Analysis of PDEs Differential Geometry Primary: 53A04, Secondary: 49Q10, 53E40 |
| url | https://arxiv.org/abs/2409.17877 |