Harmonic Maps and Minimal Immersions with Symmetries: Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM-130) (Annals of Mathematics Studies, 130) - Softcover
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Inhaltsangabe
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.
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Über die Autorin bzw. den Autor
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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Harmonic Maps and Minimal Immersions with Symmetries : Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems (Annals of Mathematics Studies, No. 130)
Verlag:
Princeton University Press, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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Harmonic Maps and Minimal Immersions with Symmetries: Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems
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Princeton University Press, Princeton, New Jersey, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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Paperback. Zustand: Very Good. Princeton, New Jersey: Princeton University Press, 1993. 228 pp. 23.5 x 15.5 cm. Glossy stiff paper wrappers, printed orange with black titling. Some faint rubbing to covers. Interior is clean and unmarked. Binding sound with no creases or cracks. . Soft Cover. Very Good. Artikel-Nr. 627575
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Harmonic Maps and Minimal Immersions with Symmetries
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Princeton University Press, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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Harmonic maps and minimal immersions with symmetries : methods of ordinary differential equations applied to elliptic variational problems / James Eells and Andrea Ratto
Verlag:
Princeton, N.J. : Princeton University Press, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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1st edition. Fine paperback copy. Particularly and surprisingly well-preserved; tight, bright, clean and especially sharp-cornered. Physical description; 228 pp., illustrations, 25 cm. Notes; Annals of mathematics studies, no. 130. Includes bibliographical references (pp. 213-223) and index. Contents; Introduction -- Pt. I Basic Variational and Geometrical Properties -- Ch. I Harmonic maps and minimal immersions -- Basic properties of harmonic maps (starting p. 13) -- Minimal immersions (starting p. 20) -- Ch. II Immersions of parallel mean curvature -- Parallel mean curvature (starting p. 24) -- Alexandrov's theorem (starting p. 29) -- Ch. III Surfaces of parallel mean curvature -- Theorems of Chern and Ruh-Vilms (starting p. 34) -- Theorems of Almgren-Calabi and Hopf (starting p. 37) -- On the Sinh-Gordon equation (starting p. 40) -- Wente's theorem (starting p. 42) -- Ch. IV Reduction techniques -- Riemannian submersions (starting p. 48) -- Harmonic morphisms and maps into a circle (starting p. 51) -- Isoparametric maps (starting p. 54) -- Reduction techniques (starting p. 58) -- Pt. II G-Invariant Minimal and Constant Mean Curvature Immersions -- Ch. V First examples of reductions -- G-equivariant harmonic maps (starting p. 64) -- Rotation hypersurfaces in spheres (starting p. 74) -- Constant mean curvature rotation hypersurfaces in R[superscript n] (starting p. 81) -- Ch. VI Minimal embeddings of hyperspheres in S[superscript 4] -- Derivation of the equation and main theorem (starting p. 92) -- Existence of solutions starting at the boundary (starting p. 95) -- Analysis of the O.D.E. and proof of the main theorem (starting p. 102) -- Ch. VII Constant mean curvature immersions of hyperspheres into R[superscript n] -- Statement of the main theorem (starting p. 111) -- Analytical lemmas (starting p. 114) -- Proof of the main theorem (starting p. 120) -- Pt. III Harmonic Maps Between Spheres -- Ch. VIII Polynomial maps -- Eigenmaps S[superscript m] [actual symbol not reproducible] S[superscript n] (starting p. 129) -- Orthogonal multiplications and related constructions (starting p. 137) -- Polynomial maps between spheres (starting p. 143) -- Ch. IX Existence of harmonic joins -- The reduction equation (starting p. 151) -- Properties of the reduced energy functional J (starting p. 154) -- Analysis of the O.D.E. (starting p. 157) -- The damping conditions (starting p. 161) -- Examples of harmonic maps (starting p. 167) -- Ch. X The harmonic Hopf construction -- The existence theorem (starting p. 171) -- Examples of harmonic Hopf constructions (starting p. 179) -- [pi][subscript 3](S[superscript 2] and harmonic morphisms (starting p. 182) -- Appendix 1 Second variations (starting p. 188) -- Appendix 2 Riemannian immersions S[superscript m] [actual symbol not reproducible] S[superscript n] (starting p. 200) -- Appendix 3 Minimal graphs and pendent drops (starting p. 204) -- Appendix 4 Further aspects of pendulum type equations (starting p. 208) -- References (starting p. 213) -- Index (starting p. 224). Subjects; Harmonic maps. Immersions (Mathematics). Differential equations, Elliptic Numerical solutions. Calcul variation. Construction harmonique Hopf. 1 Kg. Artikel-Nr. 385201
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Harmonic Maps and Minimal Immersions with Symmetries. Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems.
Verlag:
Princeton University Press, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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Paperback. Zustand: Very Good. Series: Annals of Mathematical Studies. 228p bright orange paperback, very good condition, minimal wear, slight creasing along edges, spine sunned, binding firm, pages clear and bright, free from highlighting and handwriting, a very good copy Language: English Weight (g): 340. Artikel-Nr. 233610
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Annals of Mathematics Studies: Harmonic Maps and Minimal Immersions With Symmetries: Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems (Volume 130)
Verlag:
Princeton University Press, 1993
ISBN 10: 069110249X
ISBN 13: 9780691102498
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Zustand: Good. Volume 130. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Re-bound by library. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,550grams, ISBN:9780691102498. Artikel-Nr. 5764564
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Harmonic Maps and Minimal Immersions with Symmet Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM130)
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