2024/09/17 by Alexander Bednarek, Bednarek, Alexander · 2 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2409.11608
We consider the Kähler-Ricci flow (X, ω(t))t ∈ [0,T) on a compact manifold where the time of singularity, T, is finite. We assume the existence of a holomorphic map from the Kähler manifold X to some analytic variety Y which admits a Kähler metric on a neighbourhood of the image of X and that the pullback of this metric yields the limiting cohomology class along the flow. This is satisfied, for instance, by the assumption that the initial cohomology class is rational, i.e., [ω0] ∈ H1,1(X,ℚ). Under these assumptions we prove an L4-like estimate on the behaviour of the Ricci curvature and that the Riemannian curvature is Type I in the L2-sense.