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arXiv · 1602.08983

K-stability for K\"ahler Manifolds

Ruadhaí Dervan·Julius Ross
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Abstract

We formulate a notion of K-stability for K\"ahler 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 K\"ahler 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 K\"ahler case, giving a simpler proof of this K-stability statement.

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BibTeXRIS

Ruadhaí Dervan, Julius Ross. 2016-02-29. K-stability for K\"ahler Manifolds. https://arxiv.org/abs/1602.08983

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