K-stability for Kähler manifolds

Dervan, R. and Ross, J. (2017) K-stability for Kähler manifolds. Mathematical Research Letters, 24(3), pp. 689-739. (doi: 10.4310/MRL.2017.v24.n3.a5)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dervan, Dr Ruadhaí
• Authors: Dervan, R., and Ross, J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematical Research Letters
• Publisher: International Press
• ISSN: 1073-2780
• ISSN (Online): 1945-001X