Schlicht envelopes of holomorphy and foliations by lines
| dc.creator | Larusson, Finnur | |
| dc.creator | Shafikov, Rasul | |
| dc.date | 2008-02-06 | |
| dc.date | 2008-08-08 | |
| dc.date.accessioned | 2026-07-07T09:55:16Z | |
| dc.date.available | 2026-07-07T09:55:16Z | |
| dc.description | Given a domain Y in a complex manifold X, it is a difficult problem with no general solution to determine whether Y has a schlicht envelope of holomorphy in X, and if it does, to describe the envelope. The purpose of this paper is to tackle the problem with the help of a smooth 1-dimensional foliation F of X with no compact leaves. We call a domain Y in X an interval domain with respect to F if Y intersects every leaf of F in a nonempty connected set. We show that if X is Stein and if F satisfies a new property called quasiholomorphicity, then every interval domain in X has a schlicht envelope of holomorphy, which is also an interval domain. This result is a generalization and a global version of a well-known lemma from the mid-1980s. We illustrate the notion of quasiholomorphicity with sufficient conditions, examples, and counterexamples, and present some applications, in particular to a little-studied boundary regularity property of domains called local schlichtness. | |
| dc.description | Version 2: Terminology revised and title changed in view of information about the origins of what we now call "the schlichtness lemma" that we didn't have when we finished version 1. Version 3: A few minor changes. To appear in Journal of Geometric Analysis | |
| dc.identifier | https://arxiv.org/abs/0802.0727 | |
| dc.identifier | http://arxiv.org/abs/0802.0727 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166571 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D10 (Primary); 32A10, 32A40, 32D15, 32M25, 32Q28, 32S25, 37F75 (Secondary) | |
| dc.title | Schlicht envelopes of holomorphy and foliations by lines | |
| dc.type | text |