Proves Gromov-Hausdorff convergence of regular parts to time-slices in completed singular 3D Ricci flows plus structure results on the singular set.
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 3representative citing papers
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.
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.
citing papers explorer
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Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three
Proves Gromov-Hausdorff convergence of regular parts to time-slices in completed singular 3D Ricci flows plus structure results on the singular set.
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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.