Communications in Analysis and Geometry
Volume 15 (2007)
Miyaoka-Yau-type inequalities for Kähler-Einstein manifolds
Pages: 359 – 379
We investigate Chern number inequalities on Kähler-Einstein manifolds and their relations to uniformization. For Kähler-Einstein manifolds with $c_1$ < 0, we prove certain Chern number inequalities in the toric case. For Kähler-Einstein manifolds with $c_1$ > 0, we propose a series of Chern number inequalities, interpolating Yau's and Miyaoka's inequalities.