Geometry and Topology Seminar

A renowned conjecture—described by A. Ros as one of the nicest open problems in classical geometry—proposes that the sets minimizing the perimeter among subsets of the 3-dimensional torus R^3/Z^3 with a fixed volume v are spheres, cylinders, or stripes (depending on the value of v). An equivalent conjecture applies to isoperimetric sets in the 3-dimensional cube (0,1)^3.

In this seminar, we will review the known results, primarily due to Ritorè, and discuss recent partial progress from an ongoing project with G. Antonelli.