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There are three curves in this figure.

enter image description here

I use the followed code to fill the gap:

Emin = (6)^2 - (wk + 2)^2; Emax1 = (6)^2; Emax2 = (6)^2 - (wk - 2)^2;
p[x_, left_, right_] :=HeavisideTheta[x - left] HeavisideTheta[right - x];
Plot[{Emin p[wk, 0, 4], Emax1 p[wk, 0, 2], Emax2 p[wk, 2, 4]}, {wk, 0, 4}, 
     Filling -> {1 -> {{2}, {Pink, White}}, 1 -> {{3}, {Pink, White}}}]

Then, I get the figure, which is almost what I want. It would be better if there is no line at the boundary.

How can I fill the gap without the line at the boundary?

enter image description here

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p[x_, left_, right_] := If[left < x < right, 1, Undefined]

Plot[{Emin p[wk, 0, 4], Emax1 p[wk, 0, 2], Emax2 p[wk, 2, 4]}, {wk, 0, 4}, 
      Filling -> {1 -> {{2}, Pink}, 1 -> {{3}, Pink}}]

Mathematica graphics

Edit

You may also use for example the more idiomatic

p[x_, left_, right_] := 1 /; left < x < right

for the same purpose. What you need is a function that is constant in an interval and has no numeric value outside it, so Filling can't act.

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