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Màxims i mínims --- Transformacions de fase (Física estadística) --- Canvis de fase (Física estadística)) --- Transicions de fase (Física estadística) --- Física estadística --- Regla de les fases i equilibri --- Model d'Ising --- Mínims (Matemàtica) --- Matemàtica --- Càlcul de variacions --- Superfícies mínimes --- Phase transformations (Statistical physics) --- Data processing. --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics

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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 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.

Global analysis (Mathematics). --- Manifolds (Mathematics). --- Functions of complex variables. --- Global Analysis and Analysis on Manifolds. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Global analysis (Mathematics) --- Manifolds (Mathematics) --- Minimal surfaces. --- Surfaces, Minimal --- Maxima and minima --- Anàlisi global (Matemàtica) --- Funcions de variables complexes --- Varietats (Matemàtica) --- Superfícies mínimes --- Màxims i mínims --- Aplicacions de Gauss --- Anàlisi complexa --- Funció d'una variable complexa --- Variables complexes --- Aplicacions quasiconformes --- Funcions abelianes --- Funcions analítiques --- Funcions convexes --- Funcions de diverses variables complexes --- Funcions enteres --- Funcions meromorfes --- Funcions univalents --- Grups discontinus --- Invariants conformes --- Problemes de contorn --- Sèries de Lie --- Teoria geomètrica de funcions --- Funcions de variables reals --- Funcions el·líptiques --- Sistemes dinàmics complexos --- Topologia diferencial --- Geodèsiques (Matemàtica) --- Geometria espectral --- Teoria del punt crític (Anàlisi matemàtica) --- Varietats de dimensió infinita --- Varietats analítiques --- Geometria diferencial --- Topologia --- Varietats topològiques --- Catàstrofes (Matemàtica) --- Homeomorfismes --- Subvarietats (Matemàtica) --- Topologia de baixa dimensió --- Tor (Geometria) --- Varietats complexes --- Varietats de Calabi-Yau --- Varietats de Grassmann --- Varietats diferenciables --- Varietats de Kähler --- Varietats simplèctiques