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Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry
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Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability.
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Cited by 2 Pith papers
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Analytic Bertini theorem II --- The local case
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Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons
Uniform relative Ding stability of a Fano manifold implies the necessary numerical condition ϑ(M) < 1 for the existence of Mabuchi solitons.
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