Abstract: On a compact Kähler manifold X, a Kähler-Ricci flow (KRF) is immortal when the canonical bundle of X is numerically effective. In this case, assuming the abundance conjecture and intermediate Kodaira dimension, the collapsing behavior of the normalized KRF, as already known, poses difficulty on uniform curvature estimates. We extend known $C^0$ estimates on the scalar curvature (by Song-Tian) and Ricci curvature (recently by Hein-Lee-Tosatti) to orders up to 2, and explain the failure for higher orders in general.

Brief biography: Wenrui Kong is a third-year PhD student at NYU Courant, under the supervision of Professor Valentino Tosatti. His research interests include complex and differential geometry.

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