Compactness for manifolds and integral currents with bounded diameter and volume

By S. Wenger. 2008

64 citations recorded by the source corpus.

By Gromov’s compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class of oriented k-dimensional Riemannian manifolds (with boundary) and, more generally, integral currents in metric spaces in the sense of Ambrosio–Kirchheim and replacing the Hausdorff distance with the filling volume or flat distance, we prove an analogous compactness theorem in which however we only assume uniform bounds on volume and diameter.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f413ac34ae21c276d4cb1ac5ea6a06ed6e0d524

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In Applied Mathematics

1. C. Sormani
2. S. Wenger
3. U. Lang
4. A. Lytchak
5. Sajjad Lakzian
6. Simeon Reich
7. Eva Kopecká

In Geometry and Topology

1. C. Sormani
2. S. Wenger
3. U. Lang
4. Sajjad Lakzian
5. Simeon Reich
6. Eva Kopecká

In Mathematical Physics

1. C. Sormani
2. S. Wenger

Citations in the corpus

• The Intrinsic Flat Distance between Riemannian Manifolds and other Integral Current Spaces (2010, background): “In [33], the second author has proven the key compactness theorem for the intrinsic flat distance:”