Articles liés à Minimal Surfaces from a Complex Analytic Viewpoint
Minimal Surfaces from a Complex Analytic Viewpoint - Couverture rigide
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Synopsis
1 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.
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À propos de l'auteur
The research interests of Antonio Alarcón lie primarily in minimal surfaces, Riemann surfaces, complex geometry, and holomorphic contact geometry. His main results contribute to the study of the global theory of minimal surfaces in Euclidean spaces by using both classical and modern complex analytic methods. He also studied Bryant surfaces in the hyperbolic space, complex curves and hypersurfaces in complex Euclidean spaces, and holomorphic Legendrian curves in complex contact manifolds.
Franc Forstnerič is a complex analyst who has made major contributions to the Cauchy-Riemann geometry, the theory and applications of holomorphic automorphisms of complex Euclidean spaces and related complex manifolds with large automorphism groups, and modern Oka theory, focusing on solving nonlinear complex analytic problems in the absence of topological obstructions. In the last decade he has been applying complex analytic methods to minimal surfaces and holomorphic contact geometry.
Francisco J. López is a specialist in the global theory of minimal surfaces in complete flat manifolds, Riemann surfaces, and complex analysis. Among his main contributions are those concerning the Gauss map of minimal surfaces, the geometry of complete minimal surfaces of finite total curvature, the Calabi-Yau problem, approximation and interpolation theory, and global geometry of complex curves.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Minimal Surfaces from a Complex Analytic Viewpoint (eng)
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Minimal Surfaces From a Complex Analytic Viewpoint (Springer Monographs in Mathematics) [Hardcover] [Mar 11, 2021] Alarcón, Antonio; Forstneriä, Franc and López, Francisco J.
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Minimal Surfaces from a Complex Analytic Viewpoint
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 444 pp. Englisch. N° de réf. du vendeur 9783030690557
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Minimal Surfaces from a Complex Analytic Viewpoint
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Minimal Surfaces from a Complex Analytic Viewpoint
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Springer, Palgrave Macmillan Mär 2021, 2021
ISBN 10 : 3030690555
ISBN 13 : 9783030690557
Neuf
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 444 pp. Englisch. N° de réf. du vendeur 9783030690557
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783030690557
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