Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
Bamler,: Structure theory of non-collapsed limits of Ricci flows , (2020)
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For 3D Ricci flows, time-slices converge in the Gromov–Hausdorff sense to an intrinsic terminal time-slice, and the singular set is horizontally parabolic 1-rectifiable with time image of zero 1/2-dimensional measure.
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.
Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.
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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Gromov-Hausdorff limits of the Chern-Ricci flow on smooth Hermitian minimal models of general type
Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
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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.