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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Properties of the Intrinsic Flat Distance

Authors: J. Portegies and C. Sormani
Original publication: Algebra i Analiz, tom 29 (2017), nomer 3.
Journal: St. Petersburg Math. J. 29 (2018), 475-528
MSC (2010): Primary 53C23
Published electronically: March 30, 2018
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Abstract: In this paper written in honor of Yuri Burago, we explore a variety of properties of intrinsic flat convergence. We introduce the sliced filling volume and interval sliced filling volume and explore the relationship between these notions, the tetrahedral property and the disappearance of points under intrinsic flat convergence. We prove two new Gromov-Hausdorff and intrinsic flat compactness theorems including the Tetrahedral Compactness Theorem. Much of the work in this paper builds upon Ambrosio-Kirchheim's Slicing Theorem combined with an adapted version of Gromov's Filling Volume. We are grateful to have been invited to submit a paper in honor of Yuri Burago, in thanks not only for his beautiful book written jointly with Dimitri Burago and Sergei Ivanov but also for his many thoughtful communications with us and other young mathematicians over the years.

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Additional Information

J. Portegies
Affiliation: Max Planck Institute, for Math. in the Sciences, Inselstraße 22, 04103 Leipzig, Germany

C. Sormani
Affiliation: CUNY Graduate Center, and Lehman College, 365 Fifth Avenue, New York, New York 10016

Keywords: Intrinsic flat convergence, geometric measure theory, Riemannian geometry
Received by editor(s): June 10, 2016
Published electronically: March 30, 2018
Additional Notes: Portegies partially supported by Max Planck Institute for Mathematics in the Sciences and by Sormani’s NSF grant: DMS 1309360.
Sormani partially supported by NSF DMS 1006059 and a PSC CUNY Research Grant
Dedicated: Dedicated to Yu. D. Burago on his 80th birthday
Article copyright: © Copyright 2018 American Mathematical Society

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