Isoperimetry in the cubic torus (3D)

About this app

Which region of given volume has the least surface area in a cube with glued faces? Drag the volume and watch the best shape jump from ball to tube to slab – at the thresholds 4π/81 and 1/π two shapes tie exactly. With periodic neighbour copies, a profile chart and complements for V > ½. Result from openai/math (family 354, formalised in Lean).

Subject: Open problems, solved by AI

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