Singular Kähler-Ricci shrinkers from noncollapsed limits are complex analytic varieties with log terminal singularities, yielding geometric consequences including simple connectedness and unique tangent cones.
On the structure of noncollapsed Ricci flow limit spaces
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abstract
We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a structure theory for the corresponding Ricci flow limit spaces, showing that the regular part, where convergence is smooth, admits the structure of a Ricci flow spacetime, while the singular set has codimension at least four.
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UNVERDICTED 2representative citing papers
Establishes a Lojasiewicz inequality for pointed W-entropy near cylindrical singularities in Ricci flow and applies it to prove strong uniqueness of the cylindrical tangent flow at the first singular time under a fixed gauge.
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Singular K\"ahler-Ricci Shrinkers are Complex Analytic
Singular Kähler-Ricci shrinkers from noncollapsed limits are complex analytic varieties with log terminal singularities, yielding geometric consequences including simple connectedness and unique tangent cones.
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Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
Establishes a Lojasiewicz inequality for pointed W-entropy near cylindrical singularities in Ricci flow and applies it to prove strong uniqueness of the cylindrical tangent flow at the first singular time under a fixed gauge.