Kontinuitätssatz

Theorem.

$G\subset{\mathbb{C}}^{n}$ is pseudoconvex if and only if for any family of closed analytic discs $\{d_{\alpha}\}_{\alpha\in I}$ in $G$ with $\cup_{\alpha\in I}\partial d_{\alpha}$ being a relatively compact set in $G$ then $\cup_{\alpha\in I}d_{\alpha}$ is also a relatively compact set in $G$.

This is the analogue of one of the definitions of a convex set. Just replace pseudoconvex with convex and closed analytic discs with closed line segments.

References

• 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
• 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Kontinuitätssatz Kontinuitatssatz 2013-03-22 15:49:15 2013-03-22 15:49:15 jirka (4157) jirka (4157) 5 jirka (4157) Theorem msc 32T05 Hartogs Kontinuitätssatz Kontinuitatssatz