Communications in Analysis and Geometry

Volume 15 (2007)

Number 2

Miyaoka-Yau-type inequalities for Kähler-Einstein manifolds

Pages: 359 – 379

DOI: http://dx.doi.org/10.4310/CAG.2007.v15.n2.a6

Authors

Kwokwai Chan

Naichung Conan Leung

Abstract

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.

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