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Published online by Cambridge University Press: 24 October 2008
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.