Local continuous extension of proper holomorphic maps: low-regularity and infinite-type boundaries

DOI10.1016/J.JMAA.2024.128382arXiv2210.03001OpenAlexW4393852263MaRDI QIDQ6413119

Author name not available (Why is that?)

Publication date: 6 October 2022

Abstract: We prove a couple of results on local continuous extension of proper holomorphic maps

F : D i g h t a r r o w O m e g a

,

D, O m e g a v a r s u b s e t n e q m a t h b b C^{n}

, making local assumptions on

p a r t i a l D

and

p a r t i a l O m e g a

. The first result allows us to have much lower regularity, for the patches of

p a r t i a l D, p a r t i a l O m e g a

that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstneric--Rosay. However, our assumptions allow

p a r t i a l O m e g a

to contain boundary points of infinite type.

Full work available at URL: https://doi.org/10.1016/j.jmaa.2024.128382

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