Title: Homogenization of Steklov problems with applications to sharp isoperimetric bounds, part II.
Abstract: Traditionally, deterministic homogenisation theory uses the periodic structure of Euclidean space to describe uniformly distributed perturbations of a PDE. It has been known for years that it has many applications to shape optimisation. In this talk, I will describe how the lack of periodic structure can be overcome to saturate isoperimetric bounds for the Steklov problem on surfaces. The construction is intrinsic and does not depend on any auxiliary periodic objects or quantities. Using these methods, we obtain the existence of free boundary minimal surfaces in the unit ball with large area. I will also describe how the intuition we gain from the homogenisation construction allows us to actually construct some of them, partially verifying a conjecture of Fraser and Li. This talk is based on joint work with Alexandre Girouard (U. Laval), Antoine Henrot (U. de Lorraine) and Mikhail Karpukhin (UCI).
For zoom meeting ID and password please contact dmitry.jakobson [at] mcgill.ca