Complex Analysis III

Some recent successes in value-distribution theory.- Bergman Szeg type theory for CR structures.- Regular complex geodesics for the domain Dn=((z1, ..., zn) ? ?n : z1 + ... + zn < 1).- Subelliptic, second order differential operators.- Recent results on homogeneous complex manifolds.- Ker-Einstein metrics for the case of positive first chern class.- Algebroid reduction of Nevanlinna theory.- An infinite-dimensional generalization of the Shilov boundary and infinite dimensional analytic structures in the spectrum of a uniform algebra.- New relations between Sibony-Basener boundaries.- Picard-fuchs differential equations for the quadratic periods of Abelian integrals of the first kind.- Holomorphic families of holomorphic isometries.- Complex Monge-Amp equation and related problems.- Liouville theorems.- A final word.