Kähler manifolds with almost nonnegative curvature

  title={K{\"a}hler manifolds with almost nonnegative
  author={Man-Chun Lee and Luen-Fai Tam},
  journal={Geometry \& Topology},
In this paper, we construct local and global solutions to the Kahler-Ricci flow from a non-collapsed Kahler manifold with curvature bounded from below. Combines with the mollification technique of McLeod-Simon-Topping, we show that the Gromov-Hausdorff limit of sequence of complete noncompact non-collapsed Kahler manifolds with orthogonal bisectional curvature and Ricci curvature bounded from below is homeomorphic to a complex manifold. We also use it to study the complex structure of complete… 
Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces
  • J. Lott
  • Mathematics
    Duke Mathematical Journal
  • 2021
We give an analog of triangle comparison for Kaehler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov-Hausdorff limits.
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