Kahler manifolds with Ricci curvature lower bound
Gang Liu
TL;DR
This paper extends classical Riemannian geometry theorems to Kahler manifolds with Ricci curvature lower bounds, using a Bochner formula tailored to Kahler structures.
Contribution
It introduces Kahler-specific versions of volume comparison, diameter bounds, and gradient estimates based on Ricci curvature bounds.
Findings
Established Kahler analogues of Bishop-Gromov volume comparison
Proved Bonnet-Meyers diameter bound for Kahler manifolds
Derived Yau's gradient estimate in the Kahler setting
Abstract
On Kahler 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 Kahler structure.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations