Joshua Evan Greene

collaborators

4 papers

math.GT2026

Jordan curves inscribe a positive measure of rectangles

Joshua Evan Greene, Andrew Lobb

Suppose that $I^^{3} \subset C$ is a Jordan curve of diameter $2 R$ which encloses a region of area $A$ . We prove that there exists a subset $I \subset (0, I ¨ )$ of measure at lea…

math.SG2024

Polynomial Inscriptions

Joshua Evan Greene, Andrew Lobb

We prove that for every smooth Jordan curve $I^^{3} \subset C$ and for every set $Q \subset C$ of six concyclic points, there exists a non-constant quadratic polynomia…

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…

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 $1 + 2$ . We are motivate…