A fourth-order area-preserving curve flow in centro-equiaffine geometry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911598034026496 |
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| author | Jiang, Xinjie Pan, Shengliang Zhang, Yanlong |
| author_facet | Jiang, Xinjie Pan, Shengliang Zhang, Yanlong |
| contents | In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the initial curve, we establish the long-time existence of the flow and prove that, as $t \to +\infty$, the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of $\mathrm{SL}(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A fourth-order area-preserving curve flow in centro-equiaffine geometry Jiang, Xinjie Pan, Shengliang Zhang, Yanlong Differential Geometry 53E40 (Primary), 53A15, 53A55 (Secondary) In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the initial curve, we establish the long-time existence of the flow and prove that, as $t \to +\infty$, the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of $\mathrm{SL}(2)$. |
| title | A fourth-order area-preserving curve flow in centro-equiaffine geometry |
| topic | Differential Geometry 53E40 (Primary), 53A15, 53A55 (Secondary) |
| url | https://arxiv.org/abs/2604.14804 |