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Unfortunately,
there is no exact generalization of the Horvay-
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Cahn
2-fold solution to the 4-fold case.
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Instead,
we perform an expansion for the 4-fold correction, valid
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for
small-amplitude perturbations to a parabola of revolution.
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Horvay-Cahn
solution is written in an ellipsoidal coordinate
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system.
We transform the solution to paraboloidal coordinates, and
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expand
for small eccentricity to find the expansion for a 2-fold
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solution
in paraboloidal coordinates.
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We
then generalize the 2-fold solution to the n-fold case (n = 3,4)
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in
paraboloidal coordinates .
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