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arXiv · 1301.3961

Sequences of Open Riemannian Manifolds with Boundary

Raquel Perales·Christina Sormani
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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 "$\delta$ inner regions" which avoid the boundary by a distance $\delta$. We prove Gromov-Hausdorff compactness theorems for sequences of these "$\delta$ inner regions". We then build "glued limit spaces" out of the Gromov-Hausdorff limits of these $\delta$ interior 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.

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Raquel Perales, Christina Sormani. 2013-01-17. Sequences of Open Riemannian Manifolds with Boundary. https://doi.org/10.2140/pjm.2014.270.423

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