An extension procedure for manifolds with boundary

Jeremy Wong

Vol. 235 (2008), No. 1, 173–199

DOI: 10.2140/pjm.2008.235.173

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 2000

Primary: 53C20, 53C21

Secondary: 51K10

Milestones

Received: 2 May 2007

Accepted: 9 August 2007

Published: 1 March 2008