Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-stability for K\"ahler Manifolds   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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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th