Harmonic Mappings between Riemannian
نویسندگان
چکیده
Harmonic mappings between two Riemannian manifolds is an object of extensive study, due to their wide applications in mathematics, science and engineering. Proving the existence of such mappings is challenging because of the non-linear nature of the corresponding partial differential equations. This thesis is an exposition of a theorem by Eells and Sampson, which states that any given map from a Riemannian manifold to a Riemannian manifold with non-positive sectional curvature can be freely homotoped to a harmonic map. In particular, this proves the existence of harmonic maps between such manifolds. The technique used for the proof is the heat-flow method.
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