Abstract
We consider perturbations of the harmonic map equation in the case where the target manifold is a closed Riemannian manifold of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincar e in
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