CR-Yamabe problem, Kähler metrics and K-stability

One of the main questions in Differential Geometry is the existence of special metrics, that is, a way to measure distances, on smooth manifolds.

They are the basic objects in Differential Geometry, and can be thought of as geometric objects that can be locally approximated by the usual flat space.

The goal of CRYamKmetKstab is to investigate the existence of these special metrics on complex manifolds from the point of view of Complex Differential Geometry, by employing techniques that come from Differential Geometry, Algebraic Geometry and Geometric Analysis.

More precisely, we propose a novel way to approach constant scalar curvature Kähler metrics by drawing a connection between the so-called CR-Yamabe problem and K-stability of the manifold.