Last modified: 13 October, 2002

Abstracts of Selected Articles

Let (M, J) be a compact complex manifold of Kähler type. To each Kähler metric g is associated the Calabi energy, which is defined to be the integral of the square of the scalar curvature of g, computed with respect to the volume form of g itself. This energy functional is the simplest non-trivial energy functional on the set of Kähler forms representing a fixed deRham class, and a critical metric, if any, may be regarded as a `distinguished' representative of its class. A metric that is critical for the Calabi energy among metrics whose Kähler forms represent a fixed (1,1) class is an extremal metric (in the sense of Calabi).