Year: 2025
Author: Raquel Perales, Christina Sormani
Journal of Mathematical Study, Vol. 58 (2025), Iss. 1 : pp. 96–132
Abstract
In this paper, we consider a fixed metric space (possibly an oriented Riemannian manifold with boundary) with an increasing sequence of distance functions and a uniform upper bound on diameter. When the fixed space endowed with the point-wise limit of these distances is compact, then there is uniform and Gromov-Hausdorff (GH) convergence to this space. When the fixed metric space also has an integral current structure of uniformly bounded total mass (as is true for an oriented Riemannian manifold with boundary that has a uniform bound on total volume), we prove volume preserving intrinsic flat convergence to a subset of the GH limit whose closure is the whole GH limit. We provide a review of all notions and have a list of open questions at the end.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v58n1.25.06
Journal of Mathematical Study, Vol. 58 (2025), Iss. 1 : pp. 96–132
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Metric spaces Riemannian Gromov-Hausdorff intrinsic flat.