Advanced Search

Let M̅ be a compact Riemannian manifold with sectional curvature $K_{M̅}$ satisfying $1/5<K_{M̅}\le 1$ (resp. $2\le K_{M̅}<10$), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.