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