Convergence of Manifolds and Metric Spaces with Boundary
Location: MSRI: Simons Auditorium
"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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