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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Local Ricci curvature and ν-entropy gap theorems for Ricci shrinkers depend only on dimension, generalizing prior global results and giving a local removable singularity criterion for Ricci flow.
Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.
citing papers explorer
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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.
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Rigidity and gap theorems for Ricci shrinkers
Local Ricci curvature and ν-entropy gap theorems for Ricci shrinkers depend only on dimension, generalizing prior global results and giving a local removable singularity criterion for Ricci flow.
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Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology
Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.