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arXiv · 2210.03001

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

Annapurna Banik
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Abstract

We prove a couple of results on local continuous extension of proper holomorphic maps $F:D \rightarrow \Omega$, $D, \Omega \varsubsetneq \mathbb{C}^n$, making local assumptions on $\partial{D}$ and $\partial{\Omega}$. The first result allows us to have much lower regularity, for the patches of $\partial{D}, \partial{\Omega}$ 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 $\partial{\Omega}$ to contain boundary points of infinite type.

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Annapurna Banik. 2022-10-06. Local continuous extension of proper holomorphic maps: low-regularity and infinite-type boundaries. https://doi.org/10.1016/j.jmaa.2024.128382

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