Uryson width and volume
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 a...
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| Format: | Journal article |
| Language: | English |
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Springer Verlag
2020
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| Summary: | 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. |
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