Convergence of Manifolds and Metric Spaces with Boundary
Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016
Location: SLMath: Eisenbud Auditorium
Tags/Keywords
differential geometry
Manifolds
curvature
geodesic flow
14418
"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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