LEADER 04158nam 2200697 450 001 9910485050503321 005 20230619194232.0 010 $a3-030-69056-3 024 7 $a10.1007/978-3-030-69056-4 035 $a(CKB)4100000011794652 035 $a(DE-He213)978-3-030-69056-4 035 $a(MiAaPQ)EBC6512632 035 $a(Au-PeEL)EBL6512632 035 $a(OCoLC)1241731136 035 $a(PPN)254719570 035 $a(EXLCZ)994100000011794652 100 $a20211007d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMinimal surfaces from a complex analytic viewpoint /$fAntonio Alarco?n, Franc Forstneric?, Francisco J. Lo?pez 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (XIII, 430 p. 24 illus., 21 illus. in color.) 225 1 $aSpringer monographs in mathematics 311 $a3-030-69055-5 320 $aIncludes bibliographical references and index. 327 $a1 Fundamentals -- 2 Basics on Minimal Surfaces -- 3 Approximation and Interpolations Theorems for Minimal Surfaces -- 4 Complete Minimal Surfaces of Finite Total Curvature -- 5 The Gauss Map of a Minimal Surface -- 6 The Riemann?Hilbert Problem for Minimal Surfaces -- 7 The Calabi?Yau Problem for Minimal Surfaces -- 8 Minimal Surfaces in Minimally Convex Domains -- 9 Minimal Hulls, Null Hulls, and Currents -- References -- Index. 330 $aThis monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann?Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi?Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses. 410 0$aSpringer monographs in mathematics. 606 $aGlobal analysis (Mathematics) 606 $aFunctions of complex variables 606 $aManifolds (Mathematics) 606 $aMinimal surfaces 606 $aAnàlisi global (Matemàtica)$2thub 606 $aFuncions de variables complexes$2thub 606 $aVarietats (Matemàtica)$2thub 606 $aSuperfícies mínimes$2thub 608 $aLlibres electrònics$2thub 615 0$aGlobal analysis (Mathematics) 615 0$aFunctions of complex variables. 615 0$aManifolds (Mathematics) 615 0$aMinimal surfaces. 615 7$aAnàlisi global (Matemàtica) 615 7$aFuncions de variables complexes 615 7$aVarietats (Matemàtica) 615 7$aSuperfícies mínimes 676 $a514.74 700 $aAlarcon$b Antonio$0850058 702 $aForstneric?$b Franc 702 $aLo?pez$b Francisco J. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485050503321 996 $aMinimal surfaces from a complex analytic viewpoint$91898221 997 $aUNINA