Abstract
In this paper we construct a complete injective holomorphic immersion C → C 2 \mathbb {C}\to \mathbb {C}^2 whose image is dense in C 2 \mathbb {C}^2 . The analogous result is obtained for any closed complex submanifold X ⊂ C n X\subset \mathbb {C}^n for n > 1 n>1 in place of C ⊂ C 2 \mathbb {C}\subset \mathbb {C}^2 . We also show that if X X intersects the unit ball B n \mathbb {B}^n of C n \mathbb {C}^n and K K is a connected compact subset of X ∩ B n X\cap \mathbb {B}^n , then there is a Runge domain Ω ⊂ X \Omega \subset X containing K K which admits a complete injective holomorphic immersion Ω → B n \Omega \to \mathbb {B}^n whose image is dense in B n \mathbb {B}^n .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.