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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Sobolev Maps to the Circle - From the Perspective of Analysis, Geometry, and Topology (Hardcover, 1st ed. 2021)
Loot Price: R4,172
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Sobolev Maps to the Circle - From the Perspective of Analysis, Geometry, and Topology (Hardcover, 1st ed. 2021)
Series: Progress in Nonlinear Differential Equations and Their Applications, 96
Expected to ship within 12 - 17 working days
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The theory of real-valued Sobolev functions is a classical part of
analysis and has a wide range of applications in pure and applied
mathematics. By contrast, the study of manifold-valued Sobolev maps
is relatively new. The incentive to explore these spaces arose in
the last forty years from geometry and physics. This monograph is
the first to provide a unified, comprehensive treatment of Sobolev
maps to the circle, presenting numerous results obtained by the
authors and others. Many surprising connections to other areas of
mathematics are explored, including the Monge-Kantorovich theory in
optimal transport, items in geometric measure theory, Fourier
series, and non-local functionals occurring, for example, as
denoising filters in image processing. Numerous digressions provide
a glimpse of the theory of sphere-valued Sobolev maps. 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 newdirections 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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