On the range of R2 or R3-valued harmonic morphisms
成果类型：
Article
署名作者：
Duheille, F
署名单位：
Universite Claude Bernard Lyon 1
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
308-315
关键词：
摘要：
We prove that, under some general assumptions, the range of any nonconstant harmonic morphism from a simply connected open set U in R-n to R-3, n > 3, cannot avoid three concurrent half-lines, which is an extension to Picard's little theorem. To this end, we will prove two results concerning the windings of Brownian motion around three concurrent half-lines in R-3 and the recurrence of some domains linked with the harmonic morphism.