Higher dimensional minimal "surface" analogues of the catenoid (minimal surface between two circles) can easily be depicted on a graph of radius versus distance along the axis. I predict the neck gets thinner in higher dimensions.
For four dimensions, it can also be depicted as a collection of spheres.
We can also depict on a graph the regions where the degenerate Goldschmidt solution is minimal.
Incidentally, there are many catenoids between two rings; only one is a minimal surface. Mathworld's minimal surface of revolution article says the optimal parameters are determined by solving {y1 = a * cosh ((x1 - b) / a), y2 = a * cosh ((x2 - b) / a)} for a and b, with the x axis of revolution.
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