Journal article
Uryson width and volume
- Abstract:
- We give a short proof of a theorem of Guth relating volume of balls and Uryson width. The same approach applies to Hausdorff content implying a recent result of Liokumovich–Lishak–Nabutovsky–Rotman. We show also that for any C>0 there is a Riemannian metric g on a 3-sphere such that vol(S3,g)=1 and for any map f:S3→R2 there is some x∈R2 for which diam(f−1(x))>C, answering a question of Guth.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Authors
Bibliographic Details
- Publisher:
- Springer Verlag Publisher's website
- Journal:
- Geometric And Functional Analysis Journal website
- Volume:
- 30
- Issue:
- 2
- Pages:
- 574–587
- Publication date:
- 2020-03-28
- Acceptance date:
- 2020-02-15
- DOI:
- EISSN:
-
1420-8970
- ISSN:
-
1016-443X
Item Description
Terms of use
- Copyright holder:
- Panos Papasoglu
- Copyright date:
- 2020
- Rights statement:
- © 2020 The Author. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
- Licence:
- CC Attribution (CC BY)
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