Sasaki-Einstein metrics and K-stability

Tristan C. Collins, Gábor Székelyhidi

Published 2015-12-22Version 1

We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\"ahler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.