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On invariant domains in certain complex homogeneous spaces

Xiang-Yu Zhou — 1997

Annales de l'institut Fourier

Given a compact connected Lie group $K$ . For a relatively compact $K$ -invariant domain $D$ in a Stein $K^{ℂ}$ -homogeneous space, we prove that the automorphism group of $D$ is compact and if $K$ is semisimple, a proper holomorphic self mapping of $D$ is biholomorphic.

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