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By using Sjoerd de Vries code for circular arcs:

ClearAll[splineCircle]; 
splineCircle[m_List, r_, angles_List: {0, 2 π}] := 
 Module[{seg, ϕ, start, end, pts, w, k}, {start, end} = 
    Mod[angles // N, 2 π]; If[end <= start, end += 2 π]; 
   seg = Quotient[end - start // N, π/2]; ϕ = 
    Mod[end - start // N, π/2]; 
   If[seg == 4, seg = 3; ϕ = π/2]; 
   pts = r RotationMatrix[start].# & /@ 
     Join[Take[{{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 
         0}, {-1, -1}, {0, -1}}, 2 seg + 1], 
      RotationMatrix[seg π/2].# & /@ {{1, 
         Tan[ϕ/2]}, {Cos[ϕ], Sin[ϕ]}}]; 
   If[Length[m] == 2, pts = m + # & /@ pts, 
    pts = m + # & /@ 
      Transpose[
       Append[Transpose[pts], ConstantArray[0, Length[pts]]]]]; 
   w = Join[
     Take[{1, 1/Sqrt[2], 1, 1/Sqrt[2], 1, 1/Sqrt[2], 1}, 
      2 seg + 1], {Cos[ϕ/2], 1}]; 
   k = Join[{0, 0, 0}, Riffle[#, #] &@Range[seg + 1], {seg + 1}]; 
   BSplineCurve[pts, SplineDegree -> 2, SplineKnots -> k, 
    SplineWeights -> w]] /; Length[m] == 2 || Length[m] == 3

g1 = Graphics3D[
   Table[{Hue@0.1, 
     GeometricTransformation[
      Tube[splineCircle[{0, 0, 0}, 1, {0, 3.141592653589}], 
       1/12], {-1, 1, 1}]}, {1}], Boxed -> False];
g2 = Graphics3D[
   Table[{Hue@0.1, 
     GeometricTransformation[
      Tube[splineCircle[{0, -1, 0}, 1, {0, 3.141592653589}], 1/12], 
      RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False];
g3 = Graphics3D[
   Table[{Hue@0.1, 
     GeometricTransformation[
      Tube[splineCircle[{0, -1, -2}, 1, {0, 3.141592653589}], 1/12], 
      RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False];
g4 = Graphics3D[
   Table[{Hue@0.1, 
     GeometricTransformation[
      Tube[splineCircle[{0, 0, -2}, 1, {0, 3.141592653589}], 
       1/12], {-1, 1, 1}]}, {1}], Boxed -> False];
g4 = Show[g1, g2, g3, g4]

I plotted these four circular arcs:

bent circle

How can I make a minimal surface that describes both the space inside it, and outside it stretching out to infinity? The minimal surface should describe the object as a whole and not the four arcs individually.

share|improve this question
    
Have you seen this? indiana.edu/~minimal/archive/web/mathematica.html –  belisarius Jan 17 at 15:24
    
No I have not seen it before. –  Mats Granvik Jan 17 at 15:27
1  
It's linked in the page you referenced –  belisarius Jan 17 at 15:28

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