Minimal surfaces from a complex analytic viewpoint / Antonio Alarcón, Franc Forstnerič, Francisco J. López.

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Minimal surfaces from a complex analytic viewpoint / Antonio Alarcón, Franc Forstnerič, Francisco J. López.

9783030690564 (electronic bk.)
3030690563 (electronic bk.)
9783030690571 (print)
3030690571
9783030690588 (print)
303069058X
3030690555
9783030690557

Cham : Springer, [2021]

English

1 online resource (xiii, 430 pages).

10.1007/978-3-030-69056-4 doi

QA644

516.3/62

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed April 6, 2021).

Springer monographs in mathematics.

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