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# Convergence of Manifolds and Metric Spaces with Boundary

## Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016

January 15, 2016 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Raquel Perales (UNAM - Universidad Nacional Autonoma de Mexico)
Location: MSRI: Simons Auditorium
Tags/Keywords
• differential geometry

• Manifolds

• curvature

• geodesic flow

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 14418

Abstract

"Convergence of Manifolds and Metric Spaces with Boundary"

We study sequences of oriented Riemannian manifolds with boundary

and, more generally, integral current spaces and metric spaces
with boundary. We prove theorems demonstrating when the Gromov-Hausdorff
and Sormani-Wenger Intrinsic Flat limits of sequences of such

metric spaces agree.  Then for sequences of Riemannian manifolds with boundary we only require nonnegative Ricci curvature, upper bounds on volume, non collapsing conditions on the interior of the manifold and diameter controls on the level sets near the boundary to obtain converging subsequences where both limits coincide

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