Relative stability associated to quantised extremal Kähler metrics

Extremal Metrics and Geometric Stability

This paper grew out of my lectures at Nankai Institute as well as a few other conferences in the last few years. The purpose of this paper is to describe some of my works on extremal Kähler metrics in the last fifteen years in a more unified way. In [Ti4], [Ti2], the author developed a method of relating certain stability of underlying manifolds to Kähler-Einstein metrics. A necessary and new c...

Extremal Kähler metrics and K-stability

Kähler metrics ( II )

This paper, the second of a series, deals with the function space of all smooth Kähler metrics in any given closed complex manifold M in a fixed cohomology class. This function space is equipped with a pre-Hilbert manifold structure introduced by T. Mabuchi [10], where he also showed formally it has non-positive curvature. The previous result of the second author [4] showed that the space is a ...

Kähler Metrics on G

We study G-invariant Kähler metrics on G from the Hamiltonian point of view. As an application we show that there exist G × G-invariant Ricci-flat Kähler metrics on G for any compact semisimple Lie group G.

Kähler metrics on

We study G-invariant Kähler metrics on G from the Hamiltonian point of view. As an application we show that there exist G × G-invariant Ricci-flat Kähler metrics on G for any compact semisimple Lie group G.