We study the complete Kähler-Einstein metric of a Hartogs domain Ω̃ built on an irreducible bounded symmetric domain Ω, using a power N of the generic norm of Ω. The generating function of the Kähler-Einstein metric satisfies a complex Monge-Ampère equation with boundary condition. The domain Ω̃ is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are paramet...
