Description
I will report on joint works with Abdellah Lahdili and Carlo Scarpa, investigating a natural link between the constant scalar curvature Kähler problem on a polarized manifold and a family of CR-Yamabe problems on the associated circle bundle. We show that a CR-version of the Einstein-Hilbert functional determines, in a certain sense, the K-semistability of the polarized manifold. The talk will be mostly a gentle introduction to these notions.