L2L2-estimates on p-convex Riemannian manifolds

In this paper, we establish various L2L2-estimates for the exterior differential operator on p-convex Riemannian manifolds in the sense of Harvey and Lawson. As applications, we establish a Carleman type estimate which is uniform with respect to both weight functions and domains, and we also obtain topological restrictions for a Riemannian manifold to be p-convex.