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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On gradient Kähler Ricci shrinkers the dimension of polynomial-growth holomorphic functions and (p,0)-forms is finite, with sharp linear-growth estimates and power bounds under curvature assumptions.
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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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The dimension of polynomial growth holomorphic functions and forms on gradient K\"ahler Ricci shrinkers
On gradient Kähler Ricci shrinkers the dimension of polynomial-growth holomorphic functions and (p,0)-forms is finite, with sharp linear-growth estimates and power bounds under curvature assumptions.