| 41. | Hamilton had shown that the area of a minimal surface decreases as the manifold undergoes Ricci flow.
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| 42. | Note that a bubble is a minimum energy surface but not a minimal surface by definition ).
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| 43. | It is a minimal surface, meaning that it occupies the least area when bounded by a closed space.
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| 44. | Surfaces in the family are singly periodic minimal surfaces with an infinite number of genus minimal surface families.
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| 45. | Such discretizations are often used to approximate minimal surfaces numerically, even if no closed form expressions are known.
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| 46. | The sculptures, it turned out, were " minimal surfaces, " a surface that curves in a specific way.
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| 47. | On a minimal surface the curvature along the principal curvature planes are equal and opposite at every point.
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| 48. | Surfaces in the family are singly periodic minimal surfaces with an infinite number of genus minimal surface families.
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| 49. | This surface is called a minimal surface and it, too, can be found using the calculus of variations.
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| 50. | It can also produce products with exceptional surface qualities and low tolerances with minimal surface finishing or machining required.
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