تقرير
Square pegs between two graphs
| العنوان: | Square pegs between two graphs |
|---|---|
| المؤلفون: | Greene, Joshua Evan, Lobb, Andrew |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, Mathematics - Combinatorics, Mathematics - Geometric Topology, Mathematics - Metric Geometry |
| الوصف: | 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. Comment: 28 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.07798 |
| رقم الأكسشن: | edsarx.2407.07798 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |