Subharmonicity of direct images and metrics on stable reflexive sheaves

这一研究项目的主要动机是Campana-Höring-Peternell关于稳定的自反Q-层的Bogomolov不等式的猜想。这一猜想的解将导致三维Kähler情形中的主成分分析的完成。我们的出发点是郭丰在Monge-Ampère理论方面取得的重要进展。此外，我们打算推广直接像素层的次谐和性的结果，并系统地研究无挠相干层上的度量的概念。为此，我们运用了几何分析中的L^2理论和方法。

The main motivation of this research project is a conjecture due to Campana-Höring-Peternell about the Bogomolov inequality for stable, reflexive Q-sheaves. The solution of this conjecture would lead to the completion of the MMP in the Kähler case in dimension three. Our starting point are the recent important advances in Monge-Ampère theory achieved by the Guo-Phong.Furthermore, we intend to generalize results on subharmonicity of direct image sheaves and systematically investigate concepts for metrics on torsion-free coherent sheaves. For this we use L^2 theory and methods from geometric analysis.