A geometric property of quadrilaterals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911787432017920 |
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| author | Garitsis, Efstathios Konstantinos Chrontsios Hinkkanen, Aimo |
| author_facet | Garitsis, Efstathios Konstantinos Chrontsios Hinkkanen, Aimo |
| contents | Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove that every quadrilateral with modulus in an interval $[1/K, K]$, where $K>1$, contains a disk lying in its interior, of radius depending only on the internal distances between the pairs of opposite sides of the quadrilateral and on $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A geometric property of quadrilaterals Garitsis, Efstathios Konstantinos Chrontsios Hinkkanen, Aimo Complex Variables Metric Geometry Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove that every quadrilateral with modulus in an interval $[1/K, K]$, where $K>1$, contains a disk lying in its interior, of radius depending only on the internal distances between the pairs of opposite sides of the quadrilateral and on $K$. |
| title | A geometric property of quadrilaterals |
| topic | Complex Variables Metric Geometry |
| url | https://arxiv.org/abs/2303.17337 |