Zhuang-Dan Guan
UC Riverside

Extremal metrics and geodesic stability principles

Similar to the situation of the existence of Hermitian-Einstein metrics on vector bundles, one might expect a relation between the existence of K\"ahler-Einstein metrics and certain stability on a K\"ahler manifolds. With many examples at hand we should see that there is a relation between the existence of an extremal metric(following Calabi) in a K\"ahler class and the geodesic stability of the given K\"ahler class. The uniqueness is always expected.