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What is the problem related to the following plot?

Definition of geometry

RR = ImplicitRegion[((Sqrt[x^2 + y^2] - 9))^2 + z^2 <= 1, {x, y, z}];
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    $\begingroup$ Shouldn't you tell us the problem and ask us to fix it? $\endgroup$
    – Michael E2
    Oct 13 '20 at 13:07
  • $\begingroup$ Please keep your original question,don't delete it. $\endgroup$
    – cvgmt
    Dec 17 '20 at 22:57
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You can set z=0.1 and creat a 2D ImplicitRegion instead of 3D ImplicitRegion

At the same time the SliceDensityPlot3D also need to set z == 0.1

Table[DensityPlot[
  funs[[i]][x, y, 0.1], {x, y} ∈ 
   ImplicitRegion[((Sqrt[x^2 + y^2] - 9))^2 + .1^2 <= 1, {x, y}], 
  PlotLabel -> vals[[i]], ColorFunction -> Hue, 
  PlotLegends -> Automatic, PlotRange -> All], {i, 1, 4}]

Table[SliceDensityPlot3D[funs[[i]][x, y, z], z == 0.1, 
  Element[{x, y, z}, RR], PlotRange -> All, PlotLabel -> vals[[i]], 
  PlotTheme -> "Minimal"], {i, Length[vals]}]

enter image description here

enter image description here

It seems that DensityPlot3D some times faster than 2D?

DensityPlot3D[funs[[3]][x, y, z], {x, y, z} ∈ RR]
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