An Extension Procedure for Manifolds with Boundary
نویسنده
چکیده
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 home-omorphism 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.
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تاریخ انتشار 2008