05175nam 22013215 450 991015475470332120190708092533.01-4008-8250-810.1515/9781400882502(CKB)3710000000618934(SSID)ssj0001651286(PQKBManifestationID)16426355(PQKBTitleCode)TC0001651286(PQKBWorkID)12346503(PQKB)10549274(MiAaPQ)EBC4738790(DE-B1597)468032(OCoLC)954123605(OCoLC)990753639(DE-B1597)9781400882502(EXLCZ)99371000000061893420190708d2016 fg engurcnu||||||||txtccrHarmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM-130) /Andrea Ratto, James EellsPrinceton, NJ : Princeton University Press, [2016]©19931 online resource (235 pages) illustrationsAnnals of Mathematics Studies ;312Bibliographic Level Mode of Issuance: Monograph0-691-10249-X 0-691-03321-8 Includes bibliographical references and index.Frontmatter -- INTRODUCTION -- TABLE OF CONTENTS -- PART 1. BASIC VARIATIONAL AND GEOMETRICAL PROPERTIES -- PART 2. G-INVARIANT MINIMAL AND CONSTANT MEAN CURVATURE IMMERSIONS -- PART 3. HARMONIC MAPS BETWEEN SPHERES -- APPENDIX 1. SECOND VARIATIONS -- APPENDIX 2. RIEMANNIAN IMMERSIONS Sm → Sn -- APPENDIX 3. MINIMAL GRAPHS AND PENDENT DROPS -- APPENDIX 4. FURTHER ASPECTS OF PENDULUM TYPE EQUATIONS -- REFERENCES -- INDEXThe 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.Annals of mathematics studies ;no. 130.Harmonic mapsImmersions (Mathematics)Differential equations, EllipticNumerical solutionsArc 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 and topology.Geometry.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.Harmonic maps.Immersions (Mathematics)Differential equations, EllipticNumerical solutions.514/.7Eells James, 53435Ratto Andrea, DE-B1597DE-B1597BOOK9910154754703321Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 1302788800UNINA