Abstract
We construct local and global solutions to the Kähler–Ricci flow from a noncollapsed Kähler manifold with curvature bounded from below. Combining with the mollification technique of McLeod–Simon–Topping, we show that the Gromov–Hausdorff limit of a sequence of complete noncompact noncollapsed Kähler manifolds with orthogonal bisectional curvature and Ricci curvature bounded from below is homeo-morphic 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1979-2015 |
| Number of pages | 37 |
| Journal | Geometry and Topology |
| Volume | 25 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2021 |
Funding
Acknowledgements The authors are grateful to Raphaël Hochard for sending us his thesis and generously sharing his ideas. The authors would like to thank the referee for some useful comments. Part of the work was done when Lee visited the Institute of Mathematical Sciences at The Chinese University of Hong Kong, which he would like to thank for the hospitality. Lee is supported in part by NSF grant 1709894. Tam is supported in part by Hong Kong RGC General Research Fund #CUHK 14301517.
ASJC Scopus subject areas
- Geometry and Topology