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Minimum growth of harmonic functions and thinness of a set

Published online by Cambridge University Press:  24 October 2008

Jang-Mei G. Wu
Jang-Mei G. Wu
Affiliation:
University of Illinois, Urbana, IL 61801, U.S.A.
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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

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References

REFERENCES

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