Visibility domains that are not pseudoconvex

Abstract

The earliest examples of visibility domains, given by Bharali--Zimmer, are pseudoconvex. In fact, all known examples of visibility domains are pseudoconvex. We show that there exist non-pseudoconvex visibility domains. We supplement this proof by a general method to construct a wide range of non-pseudoconvex, hence non-Kobayashi-complete, visibility domains.

7 pages; Section 1 restructured significantly; Theorem 3.1 of v1 now presented as Theorem 1.3 and Theorem 1.4 of v1 now Corollary 1.5. Published in Bul. Sci. Math.; DOI of the published journal article given elsewhere on this page>>