Log contour Plot does not plot the whole range

Question

I have the following code:

P = 100;(*Precision for the calculation*)

nV = 2;

omV = 1;(*eV*)

B0V = 194;(*eV^2*)

km[om0_, ma0_, n0_, g0_] := 
 Block[{ma = SetPrecision[ma0, P], om = SetPrecision[om0, P], 
   n = SetPrecision[n0, P], g = SetPrecision[g0, P]}, 
  Sqrt[om^2/
    2*( -ma^2/om^2 + n^2 + 1 - 
      Sqrt[(ma^2/om^2 + n^2 - 1)^2 + (2*g*194/om*10^(-9))^2])]]

pkm=ContourPlot[km[1,m,2,g],{m,10^(-4),10^0},{g,10^(-4),10^8},ScalingFunctions->{"Log","Log"},PlotLegends->BarLegend[{Automatic,{0,1}},LegendLabel->"Subscript[k, -]"],Contours->10,PlotPoints->100];

test = LogLogPlot[
  1/B0V*10^9*omV*nV*Sqrt[1 - m^2/omV^2], {m, 10^(-0.25), 10^0}, 
  PlotPoints -> 60000]

Show[pkm,  test]

that produces the following output:

My problem is that Mathematica does not color the whole range that should be colored. For example the whole range up to 1 on the x axis should be colored. I have indicate this with the blue curve. Everything under the blue curve should be colored. Everything else should give an imaginary value and should be white. (Another small question would be How I can draw the blue curve down to 0.001 y values?)

Many thanks in advance!

Answer 1

If we add the option PlotRange->All to ContourPlot,

Show[pkm, test]

gives