Let Ω be a bounded domain in C~n. The Bergman metric on Ω is a Kahler metric in- variant under the group Aut (Ω) of biholomorphic automorphisms of Ω. Denote the Bergman metric on Ω by ds~2 _Ω, and denote its Kahler form by ω. For 0 ≤ p, q≤ n We denote by H~p,q _2 (Ω) the space of square integrable harmonic (p, q)-forms on Ω With respect to ds~2 _Ω. When the boundary of Ω is smooth, Donnelly and Fefferman Proved the following result. THEOREM [DF]. If Ω is a strictly pseudoconvex domain in C~n, then Formula (cell) (1.1) See also [D], where Donnelly gave an alternative proof of this theorem using a Criterion of Gromov [Gro].
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