Colloquium
3:00 p.m., Friday (February 24, 2006)
MATX 1100
Xiuxiong Chen
University of Wisconsin, Madison
On the greatest lower bound of the Calabi energy
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.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).
