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Record Nr. |
UNISA996466557203316 |
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Autore |
Alarcon Antonio |
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Titolo |
Minimal surfaces from a complex analytic viewpoint / / Antonio Alarcón, Franc Forstnerič, Francisco J. López |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (XIII, 430 p. 24 illus., 21 illus. in color.) |
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Collana |
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Springer monographs in mathematics |
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Disciplina |
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Soggetti |
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Global analysis (Mathematics) |
Functions of complex variables |
Manifolds (Mathematics) |
Minimal surfaces |
Anàlisi global (Matemàtica) |
Funcions de variables complexes |
Varietats (Matemàtica) |
Superfícies mínimes |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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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. |
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2. |
Record Nr. |
UNICAMPANIAVAN0175837 |
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Autore |
Lekner, John |
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Titolo |
Theory of Reflection : Reflection and Transmission of Electromagnetic, Particle and Acoustic Waves / John Lekner |
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Pubbl/distr/stampa |
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Titolo uniforme |
Theory of reflection of electromagnetic and particle waves |
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Edizione |
[2. ed] |
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Descrizione fisica |
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xiv, 538 p. : ill. ; 24 cm |
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Soggetti |
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81-XX - Quantum theory [MSC 2020] |
78-XX - Optics, electromagnetic theory [MSC 2020] |
78A45 - Diffraction, scattering [MSC 2020] |
76D33 - Waves for incompressible viscous fluids [MSC 2020] |
74J20 - Wave scattering in solid mechanics [MSC 2020] |
82D10 - Statistical mechanical studies of plasmas [MSC 2020] |
78A40 - Waves and radiation in optics and electromagnetic theory [MSC 2020] |
35Q41 - Time-dependent Schrödinger equations and Dirac equations [MSC 2020] |
74J25 - Inverse problems for waves in solid mechanics [MSC 2020] |
78A46 - Inverse problems (including inverse scattering) in optics and electromagnetic theory [MSC 2020] |
78M35 - Asymptotic analysis in optics and electromagnetic theory [MSC 2020] |
81U15 - Exactly and quasi-solvable systems arising in quantum theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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