Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 577-591
University College Dublin, School of Mathematical Sciences
Belfield, Dublin 4, Ireland; joanna.t.pres 'at' gmail.com, joanna.pres 'at' ucd.ie
Abstract. This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical semi-infinite lines.) It characterizes, in terms of the spacing between the hyperplanes, those domains for which there exist minimal harmonic functions with a certain exponential growth.
2010 Mathematics Subject Classification: Primary 31B25, 31C35.
Key words: Minimal harmonic functions, comb-like domain, harmonic measure.
Reference to this article: J. Pres: Positive harmonic functions on comb-like domains. Ann. Acad. Sci. Fenn. Math. 36 (2011), 577-591.
doi:10.5186/aasfm.2011.3630
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