Families of Proper Holomorphic Embeddings and Carleman-Type Theorem with parameters
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3065709Utgivelsesdato
2023Metadata
Vis full innførselSamlinger
Originalversjon
Di Salvo, G. D., Ritter, T., & Fornæss Wold, E. (2023). Families of Proper Holomorphic Embeddings and Carleman-Type Theorem with parameters. The Journal of Geometric Analysis, 33(3), 75. 10.1007/s12220-022-01110-ySammendrag
We solve the problem of simultaneously embedding properly holomorphically into C2 a whole family of n-connected domains Omega_r in P1 such that none of the components of P1 \ Omega_r reduces to a point, by constructing a continuous mapping such that is a proper holomorphic embedding for every r. To this aim, a parametric version of both the Andersén–Lempert procedure and Carleman’s Theorem is formulated and proved.