3 papers
math.MG2026
Certified Geometry and Admissible Motion of Gerver's Sofa
Dawid Trela
The moving sofa problem asks for the largest planar set that can pass through a unit-width right-angled hallway. Gerver's 1992 construction remains the largest explicit example, bu…
math.MG2026
KKT Stresses, Affine Moments, and Separator Flux in the Heilbronn Triangle Problem
Dawid Trela
For n points in the unit square, the Heilbronn triangle problem asks for the largest possible minimum triangle area. We develop a variational stress theory for this max-min problem…
math.MG2026
Boundary Layers and Sharp Asymptotics for Maximum-Area Small Polygons
Dawid Trela
A small polygon is a planar polygon of diameter at most one; let be the largest area at order . Using the global characterization of the even-order maximizers established…