Two Reports on Harmonic MapsHarmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and K hlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers. |
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2-sphere 3-manifolds algebra class of maps closed geodesic Composition properties curvature restrictions deformed denoted differentials of order Dirichlet problem Eells-Sampson energy functional Euclidean Euler-Lagrange examples of harmonic Existence of harmonic existence theorem flat manifolds Gauss maps Grassmannians harmonic 1-form harmonic diffeomorphisms harmonic functions harmonic maps harmonic morphisms holomorphic function holomorphic maps homotopy class infinite dimensional integral periods J. H. Sampson James Eells Kähler manifolds London Mathematical Society Luc Lemaire manifolds of nonpositive manifolds with boundary map between Riemannian maps between spheres maps between surfaces Maps into flat Maps into manifolds Maps into spheres maps of manifolds maps of surfaces mean curvature minimal embeddings minimal graphs minimal immersions minimal maps minimal surfaces Operators on vector point xe Regularity theory REPORT ON HARMONIC Riemannian manifolds Riemannian sectional curvature Sacks-Uhlenbeck smooth tangent vector bundle Teichmüller tension field theorem for Riem Theorem of Lemaire topology totally geodesic maps twistor variational theory Yes-if dim Yes-provided