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arXiv · 1903.05939

Local curvature estimates of long-time solutions to the K\"ahler-Ricci flow

Frederick Tsz-Ho Fong·Yashan Zhang
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Abstract

We study the local curvature estimates of long-time solutions to the normalized K\"ahler-Ricci flow on compact K\"ahler manifolds with semi-ample canonical line bundles. Using these estimates, we prove that on such a manifold, the set of singular fibers of the semi-ample fibration on which the Riemann curvature blows up at time-infinity is independent of the choice of the initial K\"ahler metric. Moreover, when the regular fiber of the semi-ample fibration is not a finite quotient of a torus, we determine the exact curvature blow-up rate of the K\"ahler-Ricci flow near the regular fiber.

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Frederick Tsz-Ho Fong, Yashan Zhang. 2019-03-14. Local curvature estimates of long-time solutions to the K\"ahler-Ricci flow. https://arxiv.org/abs/1903.05939

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