Hyperconvexity of non-smooth pseudoconvex domains

Xu Wang¹

¹ Department of Mathematics Tongji University Shanghai, 200092, China

Annales Polonici Mathematici, Tome 111 (2014) no. 1, pp. 1-11

Résumé

We show that a bounded pseudoconvex domain $D\subset {\mathbb C}^n$ is hyperconvex if its boundary $\partial D$ can be written locally as a complex continuous family of log-Lipschitz curves. We also prove that the graph of a holomorphic motion of a bounded regular domain $\varOmega \subset {\mathbb C}$ is hyperconvex provided every component of $\partial \varOmega $ contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.

Détail

DOI : 10.4064/ap111-1-1

Keywords: bounded pseudoconvex domain subset mathbb hyperconvex its boundary partial written locally complex continuous family log lipschitz curves prove graph holomorphic motion bounded regular domain varomega subset mathbb hyperconvex provided every component partial varomega contains least points furthermore hyperconvexity lder homeomorphic invariant planar domains