Pansu-Wulff shapes in the Heisenberg group

Julian Pozuelo, Universidad de Granada, Spain

In-Person Talk 

Wulff shapes in Euclidean space are minimizers of anisotropic functionals under a volume constraint. These functionals model the shape of crystals formed by minimizing the Gibbs free energy and have been studied using different techniques such as convex geometry and calculus of variations. In this talk we will discuss recent works about anisotropic functionals defined in the sub-Riemannian Heisenberg group, we will present Pansu-Wulff shapes and give some partial results that suggest Pansu-Wulff shapes are minimizers of these anisotropic sub-Riemannian functionals. These results include joint works with Andrea Pinamonti, Gianmarco Giovannardi, Manuel Ritoré and Simone Verzellesi.