Lectures on curve shortening flow
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912998648446976 |
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| author | Haslhofer, Robert |
| author_facet | Haslhofer, Robert |
| contents | The curve shortening flow is a geometric heat equation for curves and provides an accessible setting to illustrate many important concepts from nonlinear partial differential equations, including maximum principle estimates, monotonicity formulas, Harnack inequalities and blowup analysis. All these techniques will be combined to give an exposition of Huisken's proof of Grayson's beautiful theorem that the curve shortening flow shrinks any closed embedded curve in the plane to a round point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lectures on curve shortening flow Haslhofer, Robert Analysis of PDEs Differential Geometry The curve shortening flow is a geometric heat equation for curves and provides an accessible setting to illustrate many important concepts from nonlinear partial differential equations, including maximum principle estimates, monotonicity formulas, Harnack inequalities and blowup analysis. All these techniques will be combined to give an exposition of Huisken's proof of Grayson's beautiful theorem that the curve shortening flow shrinks any closed embedded curve in the plane to a round point. |
| title | Lectures on curve shortening flow |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2604.01981 |