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On a potential-theoretic example of Kiang

Published online by Cambridge University Press:  24 October 2008

H. B. Griffiths
H. B. Griffiths
Affiliation:
Department of Pure Mathematics, The University, Birmingham 15
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Extract

In (6), Kiang gives an example of a simply connected (closed) region D in 3-space R3, bounded by a smooth 2-sphere ∂D, whose (harmonic) Green's function Γ has a critical point for any choice of pole p ∈ Int D—contrary to the analogous 2-dimensional situation. It is not known whether any position of p exists, for which Γ is non-degenerate in the sense of Morse theory; however, we show here the following result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 43 - 46
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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