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Space of Ricci flows (II)

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arxiv 1405.6797 v4 pith:M2ND65VL submitted 2014-05-27 math.DG

Xiuxiong Chen , Bing Wang This is my paper · ORCID
classification math.DG
keywords theoryahlerconjectureflowsnon-collapsedriccistructureapplications
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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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  1. The K\"ahler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations

    math.DG 2019-09 conditional novelty 7.0 of 10

    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.

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