Overview
- First monograph to offer a unified and comprehensive treatment of Sobolev maps to the circle
- Explores surprising connections with other areas of mathematics, such as optimal transport, geometric measure theory, and image processing
- Open problems are presented throughout to suggest and encourage new research directions
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 96)
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Table of contents (15 chapters)
Keywords
About this book
Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The “Complements and Open Problems” sections provide short introductions to various subsequent developments or related topics, and suggest new
directions of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena.
Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.
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Authors and Affiliations
Bibliographic Information
Book Title: Sobolev Maps to the Circle
Book Subtitle: From the Perspective of Analysis, Geometry, and Topology
Authors: Haim Brezis, Petru Mironescu
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-1-0716-1512-6
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2021
Hardcover ISBN: 978-1-0716-1510-2Published: 02 December 2021
eBook ISBN: 978-1-0716-1512-6Published: 01 January 2022
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XXXI, 530
Number of Illustrations: 17 b/w illustrations, 1 illustrations in colour
Topics: Analysis, Measure and Integration, Global Analysis and Analysis on Manifolds, Algebraic Topology