Asian Journal of Mathematics

Volume 18 (2014)

Number 1

Kähler manifolds with Ricci curvature lower bound

Pages: 69 – 100

DOI: http://dx.doi.org/10.4310/AJM.2014.v18.n1.a4

Author

Gang Liu (Department of Mathematics, University of California at Berkeley)

Abstract

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.

Keywords

comparison theorem, Kähler manifold

2010 Mathematics Subject Classification

53C20, 53C55

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