| 1. | For a minimal surface, the mean curvature is zero at every point.
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| 2. | Perelman proved this can't happen by using minimal surfaces on the manifold.
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| 3. | Depending on the support provided, the soap film naturally takes the minimal surface.
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| 4. | In differential geometry, the "'lidinoid "'is a triply periodic minimal surface.
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| 5. | From a mathematical point of view, soap films are considered as minimal surfaces.
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| 6. | A classic example is Catalan's minimal surface, which passes through a cycloid curve.
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| 7. | Minimal van Kampen diagrams are discrete analogues of minimal surfaces in Riemannian geometry.
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| 8. | Quasiperiodic minimal surfaces have been constructed in ! 2 ?"'S "'1.
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| 9. | He studied minimal surfaces and parametrized Enneper's minimal surfaces in 1864.
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| 10. | Many other mathematicians have since applied minimal surfaces to other problems.
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