It is proved that for n greater than or equal to 3 there exists a constant delta(n) with 1/4 less than or equal to delta(n)<1 such that if M is a simply connected Riemannian manifold of dimension n with delta(n)-pinched curvatures then for every Riemannian manifold N every stable harmonic map PHI:M->N is constant. Together with Howard's result, it shows that a simply connected sufficiently pinched Riemannian manifold is weakly E-unstable. (author). 8 refs. (Atomindex citation 20:013447)
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