2014/04/01 by Atsushi Yamamori, Yamamori, Atsushi
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1404.0309
A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in \mathbb Cn. Our main result is applied to obtain some simple criterions for the case n=3 and to prove that Braun-Kaup-Upmeier's theorem remains true for our class of quasi-circular domains.