Minimal Surfaces from a Complex Analytic Viewpoint : Springer : 9783030690588 : 303069058X : 12 Mar 2022 : This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann?Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the c