Minimal Surfaces from a Complex Analytic Viewpoint / Springer Monographs in Mathematics (PDF)
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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.
Franc Forstneric 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.
- Autoren: Antonio Alarcón , Franc Forstneric , Francisco J. López
- 2021, 1st ed. 2021, 430 Seiten, Englisch
- Verlag: Springer Nature Switzerland
- ISBN-10: 3030690563
- ISBN-13: 9783030690564
- Erscheinungsdatum: 10.03.2021
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- Grösse: 6.44 MB
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