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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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Publisher copy:
10.1007/s00039-020-00533-5

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Division:
MPLS
Department:
Mathematical Institute
Sub department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-7634-7885
Publisher:
Springer Verlag
Journal:
Geometric And Functional Analysis More from this journal
Volume:
30
Issue:
2
Pages:
574–587
Publication date:
2020-03-28
Acceptance date:
2020-02-15
DOI:
EISSN:
1420-8970
ISSN:
1016-443X
Language:
English
Keywords:
Pubs id:
1054243
Local pid:
pubs:1054243
Deposit date:
2020-02-16

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