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)

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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
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 (Online):1945-001X

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