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How to get the output graph which consider only x^2+y^2=4 (the boundary of the region only)? I found this on the Help.

Plot3D[{x^2 + y^2, -x^2 - y^2}, {x, -2, 2}, {y, -2, 2}, 
RegionFunction -> Function[{x, y, z}, x^2 + y^2 <= 4], 
BoxRatios -> Automatic]

When I change <= to ==, no output comes. Or do I need to use different command?

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There needs to be a finite thickness

Plot3D[{x^2 + y^2, -x^2 - y^2},
 {x, -2, 2}, {y, -2, 2},
 RegionFunction ->
  Function[{x, y, z}, 3.9 <= x^2 + y^2 <= 4],
 PlotPoints -> 75,
 MaxRecursion -> 6,
 BoxRatios -> Automatic]

enter image description here

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