Abstract

This paper introduces an isometric extension procedure for Riemannian manifolds with boundary, which preserves some lower curvature bound and produces a totally geodesic boundary. As immediate applications of this construction, one obtains in particular upper volume bounds, an upper intrinsic diameter bound for the boundary, precompactness, and a homeomorphism finiteness theorem for certain classes of manifolds with boundary, as well as a characterization up to homotopy of Gromov–Hausdorff limits of such a class.

Keywords

manifold with boundary, extension, Gromov–Hausdorff topology

Mathematical Subject Classification

Primary: 53C20, 53C21

Secondary: 51K10

Authors