Minimal Surfaces from a Complex Analytic Viewpoint

Minimal Surfaces from a Complex Analytic Viewpoint
ISBN-10
3030690563
ISBN-13
9783030690564
Category
Mathematics
Pages
430
Language
English
Published
2021-03-10
Publisher
Springer Nature
Authors
Franc Forstnerič, Antonio Alarcón, Francisco J. López

Description

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.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Similar books