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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2508.00352 |
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| _version_ | 1866914465409138688 |
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| author | Cernomazov, Nikita |
| author_facet | Cernomazov, Nikita |
| contents | We consider homothetic evolutions of the area-preserving curve-shortening flow (APCSF), that is, classical curve shortening flow with an additional non-local forcing term. By using known results on $λ$-curves, we prove the existence of non-circular shrinkers for this flow. In our first main result, we present a partial classification scheme, similar to the well-known Abresch-Langer classification for shrinkers of curve-shortening flow. Finally, we also deduce a saddle-point property for all non-circular (APCSF)-shrinkers analogous to the known saddle-point property of Abresch-Langer curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property Cernomazov, Nikita Differential Geometry We consider homothetic evolutions of the area-preserving curve-shortening flow (APCSF), that is, classical curve shortening flow with an additional non-local forcing term. By using known results on $λ$-curves, we prove the existence of non-circular shrinkers for this flow. In our first main result, we present a partial classification scheme, similar to the well-known Abresch-Langer classification for shrinkers of curve-shortening flow. Finally, we also deduce a saddle-point property for all non-circular (APCSF)-shrinkers analogous to the known saddle-point property of Abresch-Langer curves. |
| title | Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.00352 |