Harmonic maps and minimal immersions with symmetries : methods of ordinary differential equations applied to elliptic variational problems / James Eells and Andrea Ratto
1993, 1st edition. Princeton, N.J. : Princeton University Press. Fine paperback copy. Particularly and surprisingly well-preserved; tight, bright, clean and especially sharp-cornered. Item #385201
ISBN: 069110249X
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.
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