On the greatest lower bound of the Calabi energy.

Abstract: It is well known that the Calabi energy is locally convex near an extremal Kaehler metric and it is a very interesting and difficult question if theCalabi energy in the Kaehler class is bounded below by the energy of the extremal metric. According to a theorem of Calabi, an extremal Kaehler metricautomatically exhibits the maximal symmetry possible allowed by the underlying complex structure. In the 1990s, it is provedthat the Calabi energy of the invariant Kaehler metrics (maximal possible symmetric...) is bounded below by the absolute value of the Futaki invariant (evaluated at the Canonical extremal vector field). It is conjectured that the same lower bound holds for general metrics.In this talk, I will answer this question affirmatively.