Semi-discrete linear hyperbolic polyharmonic flows of closed polygons
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910818667331584 |
|---|---|
| author | McCoy, James Meyer, Jahne |
| author_facet | McCoy, James Meyer, Jahne |
| contents | We consider the damped hyperbolic motion of polygons by a linear semi-discrete analogue of polyharmonic curve diffusion. We show that such flows may transition any polygon to any other polygon, reminiscent of the Yau problem of evolving one curve to another by a curvature flow, before converging exponentially to a point that, under appropriate rescaling, is a planar basis polygon. We also consider a hyperbolic linear semi-discrete flow of the Yau curvature difference flow, where a polygonal curve is able to flow to any other such that we get convergence to the target polygon in infinite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-discrete linear hyperbolic polyharmonic flows of closed polygons McCoy, James Meyer, Jahne Classical Analysis and ODEs Analysis of PDEs 34A26 (Primary) 51E12, 34A30, 53E99 (Secondary) We consider the damped hyperbolic motion of polygons by a linear semi-discrete analogue of polyharmonic curve diffusion. We show that such flows may transition any polygon to any other polygon, reminiscent of the Yau problem of evolving one curve to another by a curvature flow, before converging exponentially to a point that, under appropriate rescaling, is a planar basis polygon. We also consider a hyperbolic linear semi-discrete flow of the Yau curvature difference flow, where a polygonal curve is able to flow to any other such that we get convergence to the target polygon in infinite time. |
| title | Semi-discrete linear hyperbolic polyharmonic flows of closed polygons |
| topic | Classical Analysis and ODEs Analysis of PDEs 34A26 (Primary) 51E12, 34A30, 53E99 (Secondary) |
| url | https://arxiv.org/abs/2502.04939 |