|
|||||
|
|
|
|
|
|
|
|
|
Sequences of open
Riemannian manifolds with boundary
Raquel Perales and Christina Sormani |
|
Vol. 270 (2014), No. 2, 423–471
|
Abstract |
|
We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we examine δ-inner regions, that avoid the boundary by a distance δ. We prove Gromov–Hausdorff compactness theorems for sequences of these δ-inner regions. We then build “glued limit spaces” out of the Gromov–Hausdorff limits of δ-inner regions and study the properties of these glued limit spaces. Our main applications assume the sequence is noncollapsing and has nonnegative Ricci curvature. We include open questions. |
Keywords
Gromov–Hausdorff, manifold, boundary
|
Mathematical Subject Classification 2010
Primary: 53C23
|
Milestones
Received: 8 February 2013
Revised: 18 June 2013
Accepted: 5 August 2013
Published: 22 August 2014
|
Authors |
| Raquel Perales | |
| Department of Mathematics Stony Brook University 100 Nicolls Rd Stony Brook, NY 11794 United States |
|
| Christina Sormani | |
| Department of Mathematics CUNY Graduate Center and Lehman College 365 Fifth Avenue New York, NY 10016 United States |
|
|
