Showing math.SGShow all
3 papers · 1 filter
math.SG2024
Polynomial Inscriptions
Joshua Evan Greene, Andrew Lobb
We prove that for every smooth Jordan curve and for every set of six concyclic points, there exists a non-constant quadratic polynomial…
math.SG2024
Square pegs between two graphs
Joshua Evan Greene, Andrew Lobb
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 . We are motivate…
math.SG2024
Floer homology and square pegs
Joshua Evan Greene, Andrew Lobb
We construct a version of Lagrangian Floer homology whose chain complex is generated by the inscriptions of a rectangle into a real analytic Jordan curve. By using its associated s…