For any Fano manifold, the Donaldson-Futaki invariant of its optimal degeneration is bounded below by -(1-R(X))/R(X) nV, where R(X) is the greatest Ricci lower bound.
Space of Ricci flows (II)
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abstract
Based on the compactness of the moduli of non-collapsed Calabi-Yau spaces with mild singularities, we set up a structure theory for polarized K\"ahler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed K\"ahler Einstein manifolds. As applications, we prove the Hamilton-Tian conjecture and the partial-$C^0$-conjecture of Tian.
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2019 1verdicts
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The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
For any Fano manifold, the Donaldson-Futaki invariant of its optimal degeneration is bounded below by -(1-R(X))/R(X) nV, where R(X) is the greatest Ricci lower bound.