Detect and Remove Singular Curves
The singularity of 
along the unit circle is automatically removed when plotting it.
In[1]:=
Plot3D[1/(1 - x^2 - y^2), {x, y} \[Element] Disk[{0, 0}, 2],
PlotTheme -> "Marketing", BoxRatios -> {1, 1, 1},
ClippingStyle -> None]Out[1]=
