On Bloch’s “Principle of Topological Continuity”

We discuss to what extent certain results about totally ramified values of entire and meromorphic functions remain valid if one relaxes the hypothesis that some value is totally ramified by assuming only that all islands over some Jordan domain are multiple. In particular, we prove a result suggested by Bloch which says that an entire function of order less than 1 has a simple island over at least one of two given Jordan domains with disjoint closures.

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Published in:
Computational Methods and Function Theory
Publisher:
Springer Science and Business Media LLC
Heldermann
Publishing place:
Heidelberg
Berlin
Lemgo
Vol.:
24
No.:
3
ISSN:
1617-9447
ISSN:
2195-3724
ISSN:
1617-9447
Pages:
605 - 630
Date Issued:
2024
URN:
urn:nbn:de:gbv:8:3-2026-01117-2
DOI:
10.1007/s40315-024-00531-w
Language:
English
Type of Resource:
Text
Publisher:
Springer Science and Business Media LLC
Keywords:
Meromorphic function; Entire function; Ramified value; Island; Ahlfors theory; Covering surface; Quasiconformal deformation; Line complex
Classification:
Published version
DDC subject of DNB:
510 Mathematics
Hosting institution:
Faculties, Faculty of Mathematics and Natural Sciences

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