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

Abstract

We prove a couple of results on local continuous extension of proper holomorphic maps $F:D\to \Omega$, $D,\Omega {\mathbb{C}}^n$, 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.

20 pages. Added references; added Remark 6.1. Accepted for publication in J. Math. Anal. Appl.; DOI of the published journal article given elsewhere on this page>>

References in corpus (1)

• On the continuous extension of Kobayashi isometries