Journal
ST PETERSBURG MATHEMATICAL JOURNAL
Volume 29, Issue 3, Pages 475-528Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/spmj/1504
Keywords
Intrinsic flat convergence; geometric measure theory; Riemannian geometry
Categories
Funding
- Max Planck Institute for Mathematics in the Sciences
- Sormani's NSF grant [DMS 1309360]
- NSF DMS [1006059]
- PSC CUNY Research Grant
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1006059] Funding Source: National Science Foundation
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available