Abstract
Our basic results concerning harmonic maps are parallel to those in Part I [Gro11] about minimal subvarieties. First we produce compact harmonic foliations 7-( by solving in some cases the asymptotic Dirichlet problem. Then we construct transversal measures by adopting the parabolic equation method of Eells and Sampson. Finally we indicate some applications to the rigidity and the pinching problems.
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