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The Dirichlet problem for harmonic mappings
P Matzeu Istituto Matematico UniversitÓ Via Ospedale 72 09100 Cagliari
Harmonic mappings into spheroids
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Harmonic Mappings and Minimal Immersion: Lectures given at the 1st 1984 ...
Limited preview - 2006
apply arbitrary assume assumptions boundary values bounded BR(p Christoffel symbols closed geodesic compact conformal map constant continuous converges convex curve define denotes derive diffeomorphism differential dimension Dirichlet problem Eells elliptic systems energy minimizing equations estimates for harmonic Euclidean space existence theorem Gauss map geometry harmonic coordinates harmonic diffeomorphisms hence Hildebrandt holds holomorphic homotopic homotopy class implies inequality infer Jacobi field Jost Kaul lectures Lemaire Lemma Math maximum principle mean curvature metric metric tensor minimal submanifolds minimal surfaces Moreover nonlinear nonpositive obtain orthonormal Preprint priori estimates proof of Theorem proved quadratic regular ball representation respect result Riemann normal coordinates Riemannian manifold satisfies Schoen sectional curvature sequence singular smooth subset Suppose tangent tensor Theorem 1.2 theory topological Uhlenbeck uniqueness theorem variational vector field weakly harmonic map Widman yields