Einstein-Kaehler Metric on Cartan-Hartogs Domains

摘要

Cheng and Yau[CY] proved that any C2 bounded pseudoconvex domain Ω in C~n has a complete Einstein-Kahler metric. Without any regularity assumption on the domain Ω, Mok and Yau[MY] proved that the complete Einstein-Kahler metric always exists. This Einstein-Kaehler metric is given by E_Ω(z): = Σ partial deriv~2g/partial deriv z_i partial deriv z_j dz_i dz_j, where g is a 1unique solution to the boundary problem of the Monge-Ampere equation: {det (partial deriv~2g/partial deriv z_ipartial derivz_j)=e~(n+1)g} z∈Ω g=∞ z∈partial derivΩ.