Square pegs between two graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913425400004608 |
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| author | Greene, Joshua Evan Lobb, Andrew |
| author_facet | Greene, Joshua Evan Lobb, Andrew |
| contents | We show that there always exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than $1 + \sqrt{2}$. We are motivated by Tao's result that there exists such a square in the case of Lipschitz constant less than $1$. In the case of Lipschitz constant $1$, we show that the Jordan curve inscribes rectangles of every similarity class. Our approach involves analysing the change in the spectral invariants of the Jordan Floer homology under perturbations of the Jordan curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Square pegs between two graphs Greene, Joshua Evan Lobb, Andrew Symplectic Geometry Combinatorics Geometric Topology Metric Geometry We show that there always exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than $1 + \sqrt{2}$. We are motivated by Tao's result that there exists such a square in the case of Lipschitz constant less than $1$. In the case of Lipschitz constant $1$, we show that the Jordan curve inscribes rectangles of every similarity class. Our approach involves analysing the change in the spectral invariants of the Jordan Floer homology under perturbations of the Jordan curve. |
| title | Square pegs between two graphs |
| topic | Symplectic Geometry Combinatorics Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2407.07798 |