The inverse curve shortening flow on the hyperbolic plane
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917494345695232 |
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| author | Krznarić, Ivan López, Rafael |
| author_facet | Krznarić, Ivan López, Rafael |
| contents | We study the inverse curve shortening flow in the hyperbolic plane $\h^2$. We classify all solitons with respect to parabolic and conformal vector fields of $\h^2$. In the upper half-plane model of $\h^2$, we prove that parabolic solitons are all graphs on the $y$-axis, whereas conformal solitons are graphs on the $x$-axis. We study the concavity of these solitons and when they approach the coordinate axes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14385 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The inverse curve shortening flow on the hyperbolic plane Krznarić, Ivan López, Rafael Differential Geometry 35J60, 53E10, 53C21, 53C44, 53C50, 58J05 We study the inverse curve shortening flow in the hyperbolic plane $\h^2$. We classify all solitons with respect to parabolic and conformal vector fields of $\h^2$. In the upper half-plane model of $\h^2$, we prove that parabolic solitons are all graphs on the $y$-axis, whereas conformal solitons are graphs on the $x$-axis. We study the concavity of these solitons and when they approach the coordinate axes. |
| title | The inverse curve shortening flow on the hyperbolic plane |
| topic | Differential Geometry 35J60, 53E10, 53C21, 53C44, 53C50, 58J05 |
| url | https://arxiv.org/abs/2605.14385 |