  Electrostatic Green functions for grounded equipotential circular and
elliptical rings, and grounded hyperspheres in n-dimension electrostatics, are
constructed using Sommerfeld's method. These electrostatic systems are treated
geometrically as different radial p-norm wormhole metrics that are deformed to
be the Manhattan norm, namely "squashed wormholes". Differential geometry
techniques are discussed to show how Riemannian geometry plays a rule in
Sommerfeld's method. A comparison is made in terms of strength and position of
the image charges for Sommerfeld's method with those for the more conventional
Kelvin's method. Both methods are shown to be mathematically equivalent in
terms of the corresponding Green functions. However, the two methods provide
different physics perspectives, especially when studying different limits of
those electrostatic systems. Further studies of ellipsoidal cases are
suggested.
