The Construction of Minimal Surfaces

By Pingxing Xing. 2002

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The classical theory of minimal surfaces (2011, methodology): “Along these lines, we have already mentioned the rigorous proofs by Hoffman, Weber and Wolf [83] and by Hoffman and White [85] of existence of a genus-one helicoid, a mathematical fact that was earlier computationally indicated by Hoffman, Karcher and Wei [76].”
Construction of complete embedded self-similar surfaces under mean curvature flow. Part II (2006, background): “This surface was discovered by Scherk and is the most symmetric of a one parameter family of minimal surfaces (see [4] or [11] [12]).”
Conformal properties in classical minimal surface theory (2004, background): “Recently, Pérez, Rodŕıguez and Traizet [91] proved that the space of properly embedded minimal tori with any fixed number of parallel ends(4) in T× R is a 3-dimensional manifold which consists of the examples defined by Karcher in [46, 47].”