Kähler manifolds with almost non-negative curvature

Abstract

In this paper, we construct local and global solutions to the Kähler-Ricci flow from a non-collapsed Kähler 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 Kähler 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 Kähler manifolds with nonnegative orthogonal bisectional curvature, nonnegative Ricci curvature and maximal volume growth.

32 pages

References in corpus (3)

• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II
• Kähler-Ricci Shrinkers and Ancient Solutions with Nonnegative Orthogonal Bisectional Curvature
• Gap theorem on Kähler manifold with nonnegative orthogonal bisectional curvature

Cited by in corpus (2)

• The Chern-Ricci flow
• Some local Maximum principles along Ricci Flow