Recent progress in Kähler geometry

Details Recent progress in Kähler geometry Recent progress in Kähler geometry

2003-04-18

arxiv.org/abs/math/0304262v1

Proceedings of the ICM, Beijing 2002, vol. 2, 273--282

Mathematics

Differential Geometry

Scientific paper

In recent years, there are many progress made in K\"ahler geometry. In particular, the topics related to the problems of the existence and uniqueness of extremal K\"ahler metrics, as well as obstructions to the existence of such metrics in general K\"ahler manifold. In this talk, we will report some recent developments in this direction. In particular, we will discuss the progress recently obtained in understanding the metric structure of the infinite dimensional space of Kaehler potentials, and their applications to the problems mentioned above. We also will discuss some recent on Kaehler Ricci flow.

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