Volume comparison in Kähler geometry

Volume comparison in Kähler geometry

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Yuchen Liu , Princeton University
Fine Hall 322

In Riemannian geometry, the Bishop-Gromov volume comparison theorem implies that the spheres have the maximal volume growth rate among manifolds with the same (positive) lower bounds on Ricci curvature. In the Kähler world, we may ask whether a similar volume comparison holds by replacing the spheres with the complex projective spaces. I will explain why Bishop-Gromov fails in the Kähler setting, and I will demonstrate a global volume comparison for Kähler manifolds based on a recent work by Fujita.