We survey a number of metric properties of intersections of finitely many congruent balls called ball polyhedra in Euclidean spaces. In particular, our talk is centered around the status of the shortest billiard conjecture, the global rigidity conjecture, Hadwiger's covering conjecture, and the Gromov-Klee-Wagon volumetric conjecture for ball polyhedra.
Ball polyhedra - old and new
2022. 11. 22. 10:30