Scalar curvature blows up at Type I rate at Type I singular points of general Ricci flows in all dimensions, implying no Type I singularities exist in bounded-scalar-curvature flows; similar ancient-Type-I behavior holds for ancient solutions.
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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.
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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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.