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Functions of several complex variables --- Domains of holomorphy --- Fonctions de plusieurs variables complexes --- Domaines d'holomorphie

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Symplectic geometry. --- Symplectic groups. --- Domains of holomorphy. --- Géométrie symplectique. --- Groupes symplectiques. --- Domaines d'holomorphie. --- Géométrie symplectique --- Groupes symplectiques --- Domaines d'holomorphie --- Symplectic geometry --- Symplectic groups --- Domains of holomorphy --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Groups, Symplectic --- Linear algebraic groups --- Geometry, Differential

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Domains of holomorphy. --- Functions of several complex variables. --- Pseudoconvex domains --- Domaines d'holomorphie. --- Domaines pseudo-convexes --- Fonctions de plusieurs variables complexes --- Espaces analytiques --- Espaces analytiques

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The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in mathbb{R}^n for any nge 3. These methods, which the authors develop essentially from the first principles, enable them to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to mathbb{R}^n is a real analytic Banach manifold, obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces, and show general position theorems for non-orientable conformal minimal surfaces in mathbb{R}^n. The authors also give the first known example of a properly embedded non-orientable minimal surface in mathbb{R}^4; a Möbius strip. All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in mathbb{R}^n with any given conformal structure, complete non-orientable minimal surfaces in mathbb{R}^n with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of mathbb{CP}^{n-1} in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of mathbb{R}^n.

Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} -- Local analytic geometry [See also 13-XX and 14-XX] -- Analytic subsets of affine space. --- Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} -- Holomorphic convexity -- Holomorphic and polynomial approximation, Runge pairs, interpolation. --- Sprays (Mathematics) --- Minimal surfaces. --- Holomorphic mappings. --- Approximation theory. --- Analytic spaces. --- Affine differential geometry.

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Complex analysis --- 517.5 --- Theory of functions --- Functions of several complex variables. --- Linear operators. --- 517.5 Theory of functions --- Fonctions de plusieurs variables complexes. --- Pseudoconvex domains --- Domaines pseudo-convexes --- Domains of holomorphy --- Domaines d'holomorphie --- Fonctions de plusieurs variables complexes