The nonexistence of stable submanifolds, varifolds, and harmonic maps in sufficiently pinched simply connected Riemannian manifolds (Q1074856)

The aim of this paper is to prove the following theorems: 1) There is a constant \(\delta (n,p)>1/4\) so that if \(M^ n\) is a compact simply connected strictly \(\delta\) (n,p)-pinched Riemannian manifold of dimension n, then there are no stable p-dimensional submanifolds, stable p-dimensional integral currents, or stable p-dimensional varifolds in M. 2) For each \(n\geq 3\) there is a \(\delta\) (n) with \(1/4\leq \delta (n)<1\) such that if M is a simply connected compact strictly \(\delta\) (n)- pinched Riemannian manifold of dimension n, then there are no stable harmonic maps \(\psi\) : \(N\to M\) for any compact Riemannian manifold N.