Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 (eBook)

Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM-130)

James Eells, Andrea Ratto (Autoren)

eBook Download: PDF

2016 | 1. Auflage
240 Seiten
Princeton University Press (Verlag)
978-1-4008-8250-2 (ISBN)

Infos

James Eells is Professor of Mathematics at the University of Warwick. Andrea Ratto is Professor Mathematics at the Universite de Bretagne Occidentale in Brest.

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The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: arc length • Catenary • Clifford Algebra • Codimension • coefficient • Compact space • Complex Projective Space • Connected sum • Constant Curvature • corollary • covariant derivative • Curvature • Cylinder (geometry) • Degeneracy (mathematics) • Diagram (category theory) • differential equation • Differential Geometry • Elliptic partial differential equation • Embedding • energy functional • Equation • existence theorem • existential quantification • fiber bundle • Gauss map • Geometry • Geometry and Topology • Gravitational Field • harmonic map • Hyperbola • hyperplane • hypersphere • hypersurface • Integer • Iterative Method • Levi-Civita connection • Lie group • Mathematics • Maximum principle • mean curvature • Normal (geometry) • Numerical analysis • Open set • ordinary differential equation • Parabola • quadratic form • Sign (mathematics) • Special case • stiefel manifold • submanifold • Suggestion • Surface of revolution • symmetry • tangent bundle • Theorem • vector bundle • Vector Space • Vertical tangent • Winding number
• ISBN-10: 1-4008-8250-8 / 1400882508
• ISBN-13: 978-1-4008-8250-2 / 9781400882502