Minimum growth of harmonic functions and thinness of a set
Published online by Cambridge University Press: 24 October 2008
Extract
In [3], Barth, Brannan and Hayman proved that if u(z) is any non-constant harmonic function in ℝ2, ø(r) is a positive increasing function of r for r ≥ 1 and
then there exists a path going from a finite point to ∞, such that u(z) > ø(|z|) on Γ. Moreover, they showed by example that the integral condition above cannot be relaxed.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 123 - 133
- Copyright
- Copyright © Cambridge Philosophical Society 1984
References
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