Vanishing theorems on Riemannian manifolds, and geometric applications

A general Liouville-type result and a corresponding vanishing theorem are proved under minimal regularity assumptions. The latter is then applied to conformal deformations of stable minimal hypersurfaces, to the L2 cohomology of complete manifolds, to harmonic maps under various geometric assumptions, and to the topology of submanifolds of Cartan-Hadamard spaces with controlled extrinsic geometry.