arXiv:1210.3895 [math.DG]AbstractReferencesReviewsResources
Properties of the Intrinsic Flat Distance
Published 2012-10-15, updated 2014-10-29Version 3
Here we explore the properties of Intrinsic Flat convergence, proving a number of theorems relating it to Gromov-Hausdorff convergence. We introduce the sliced filling volume and explore the relationship between this notion, the tetrahedral property and intrinsic flat convergence. We prove the Tetrahedral Compactness Theorem. Additional Bolzano-Weierstrass and Arzela-Ascoli theorems involving sliced filling volumes will be posted in future updates of this article.
Comments: v3: Arzela-Ascoli and Bolzano-Weierstrass Theorems appearing in the v2 posting have been simplified and moved to "Intrinsic Flat Arzela-Ascoli Theorems" written by Sormani alone (see arXiv:1402.6066). v3: has a new coauthor J. Portegies who has helped revise and refine theorems concerning filling volumes. More will appear in v4
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