Jordan curves inscribe a positive measure of rectangles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913042840682496 |
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| author | Greene, Joshua Evan Lobb, Andrew |
| author_facet | Greene, Joshua Evan Lobb, Andrew |
| contents | Suppose that $γ\subset \mathbb{C}$ is a Jordan curve of diameter $2R$ which encloses a region of area $A$. We prove that there exists a subset $I \subset (0,π)$ of measure at least $A/R^2$ such that if $θ\in I$, then there exist four points on $γ$ at the vertices of a rectangle whose diagonals meet at angle $θ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jordan curves inscribe a positive measure of rectangles Greene, Joshua Evan Lobb, Andrew Geometric Topology Combinatorics Symplectic Geometry Suppose that $γ\subset \mathbb{C}$ is a Jordan curve of diameter $2R$ which encloses a region of area $A$. We prove that there exists a subset $I \subset (0,π)$ of measure at least $A/R^2$ such that if $θ\in I$, then there exist four points on $γ$ at the vertices of a rectangle whose diagonals meet at angle $θ$. |
| title | Jordan curves inscribe a positive measure of rectangles |
| topic | Geometric Topology Combinatorics Symplectic Geometry |
| url | https://arxiv.org/abs/2604.17116 |