On the instability of minimal submanifolds in Riemannian manifolds of positive curvature (Q1101708)

First we show that minimal closed surfaces in sufficiently pinched, simply-connected Riemannian manifolds are unstable. This is a partial affirmative answer to the conjecture of Lawson and Simons. Next we give a sufficient condition for a relatively compact domain in a Riemannian manifold minimally immersed in a manifold of positive curvature, to be unstable.