Contents Online
Mathematical Research Letters
Volume 24 (2017)
Number 3
K-stability for Kähler manifolds
Pages: 689 – 739
DOI: https://dx.doi.org/10.4310/MRL.2017.v24.n3.a5
Authors
Abstract
We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies K-semistability (resp. uniformly K-stable). In particular this shows that the existence of a constant scalar curvature Kähler metric implies K-semistability, and K-stability if one assumes the automorphism group is discrete. We also show how Stoppa’s argument holds in the Kähler case, giving a simpler proof of this K-stability statement.
Received 10 March 2016
Accepted 15 December 2016
Published 1 September 2017