期刊
JOURNAL OF GEOMETRIC ANALYSIS
卷 28, 期 4, 页码 2927-2960出版社
SPRINGER
DOI: 10.1007/s12220-017-9942-9
关键词
Constant scalar curvature Kahler metric; K-Stability; Energy functional asymptotics; YTD conjecture
类别
We prove that constant scalar curvature Kahler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds. Relying on a recent result by R. Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover follows that cscK manifolds with discrete automorphism group are uniformly K-stable. As a main step of the proof we establish, in the general Kahler setting, a formula relating the (generalised) Donaldson-Futaki invariant to the asymptotic slope of the K-energy along weak geodesic rays.
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