Curve Shortening Flow of Space Curves with Convex Projections
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910670264467456 |
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| author | Sun, Qi |
| author_facet | Sun, Qi |
| contents | We show that under Space Curve Shortening flow any closed immersed curve in $\mathbb R^n$ whose projection onto $\mathbb{R}^2\times\{\vec{0}\}$ is convex remains smooth until it shrinks to a point. Throughout its evolution, the projection of the curve onto $\mathbb{R}^2\times\{\vec{0}\}$ remains convex.
As an application, we show that any closed immersed curve in $\mathbb R^n$ can be perturbed to an immersed curve in $\mathbb R^{n+2}$ whose evolution by Space Curve Shortening shrinks to a point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curve Shortening Flow of Space Curves with Convex Projections Sun, Qi Differential Geometry Analysis of PDEs 53E10 We show that under Space Curve Shortening flow any closed immersed curve in $\mathbb R^n$ whose projection onto $\mathbb{R}^2\times\{\vec{0}\}$ is convex remains smooth until it shrinks to a point. Throughout its evolution, the projection of the curve onto $\mathbb{R}^2\times\{\vec{0}\}$ remains convex. As an application, we show that any closed immersed curve in $\mathbb R^n$ can be perturbed to an immersed curve in $\mathbb R^{n+2}$ whose evolution by Space Curve Shortening shrinks to a point. |
| title | Curve Shortening Flow of Space Curves with Convex Projections |
| topic | Differential Geometry Analysis of PDEs 53E10 |
| url | https://arxiv.org/abs/2410.08399 |