Limits of manifolds with boundary II

Abstract

In this paper, as a continuation of [34], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of manifolds, boundaries and the second fundamental forms of boundaries, and an upper diameter bound. We describe the local geometric structure of the limit spaces, and establish some stability results including Lipschitz homotopy stability.