Asian Journal of Mathematics
Volume 18 (2014)
Kähler manifolds with Ricci curvature lower bound
Pages: 69 – 100
On Kähler manifolds with Ricci curvature bounded from below, we establish some theorems which are counterparts of some classical theorems in Riemannian geometry, for example, Bishop-Gromov’s relative volume comparison, Bonnet-Meyers theorem, and Yau’s gradient estimate for positive harmonic functions. The tool is a Bochner type formula reflecting the Kähler structure.
comparison theorem, Kähler manifold
2010 Mathematics Subject Classification