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Minimal surfaces

This time the research we conducted is minimal surfaces. For any closed curve, we can get a minimal surface. So what is the minimal surface? Local least area definition: A surface M ⊂ R^3 is minimal if and only if every point p ∈ M has a neighbourhood, bounded by a simple closed curve, which has the least area among all surfaces having the same boundary. This property is local: there might exist regions in a minimal surface, together with other surfaces of smaller area which have the same boundary. This property establishes a connection with soap films; a soap film deformed to have a wire frame as boundary will minimize area(from wiki). In simple terms, Minimal surfaces are the surfaces of the smallest area spanned by a given boundary. The equivalent is the definition that it is the surface of vanishing mean curvature. This may be incomprehensible to some people. In simple terms, it is to put a closed curve in soapy water. The bubbles formed by it are its minimal surfaces.
So as long as it is a closed curve, no matter what its shape is, there will be a minimal surface (minimal surfaces can also be formed between multiple curves). Then we can try to make some relatively rugged curves and then guess the shape of its curved surface.

Due to lack of imagination, when talking about closed curves, I can only think of circles, but after some deformations, we can get some strange shapes. After some attempts, I got a curve that seemed easier to guess.
This shape is actually the curve in the above picture. If you fold it again, it looks like the letter "C" becomes the letter "S" from the side, and it looks silky.
If you look closely, you will find that this curve is actually divided into six parts, each part is a half-circle, and then by changing the value and interval of x, y, and z, and then splicing them together to get the curve, in order to let it see It seems a little stranger. I made more changes to the part of the upper half-circle and the lower half-circle of the link. This is how the whole graph looks like from the top.
On the whole, this curve has a lot of turns, but in my opinion, there should not be many changes to its Minimal surfaces. It should only be that there are more waves at the border, and the part far away from the edge should be. It will be smoother. I think this curve can form bubbles because its curves are not interspersed, which will help the formation of Minimal surfaces. As for the guess of the appearance, it should be divided into roughly two parts. Each part is similar to the first picture in this article. There may be a straight-line connection in the middle. Of course, this is just my guess and has not been confirmed.

Finally, add a handle.
size: x: 46.88, y: 39.88, z: 135.12

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