K-Semistability for irregular Sasakian manifolds

Understand

We introduce a notion of K-semistability for Sasakian manifolds.

• This extends to the irregular case the orbifold K-semistability of Ross-Thomas.
• Our main result is that a Sasakian manifold with constant scalar curvature is necessarily K-semistable.
• As an application, we show how one can recover the volume minimization results of Martelli-Sparks-Yau, and the Lichnerowicz obstruction of Gauntlett-Martelli-Sparks-Yau from this point of view.