Geodesic
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
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

Xu Wang 1

1 Department of Mathematics Tongji University Shanghai, 200092, China 
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Xu Wang. Hyperconvexity of non-smooth pseudoconvex domains. Annales Polonici Mathematici, Tome 111 (2014) no. 1, pp. 1-11. doi : 10.4064/ap111-1-1. http://geodesic.mathdoc.fr/articles/10.4064/ap111-1-1/

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