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 ( S 3 ,...
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| Veröffentlicht in: | Geometric and functional analysis 2020-04, Vol.30 (2), p.574-587 |
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| creator | Papasoglu, Panos |
| description | 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
(
S
3
,
g
)
=
1
and for any map
f
:
S
3
→
R
2
there is some
x
∈
R
2
for which
diam
(
f
-
1
(
x
)
)
>
C
, answering a question of Guth. |
| doi_str_mv | 10.1007/s00039-020-00533-5 |
| format | Article |
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C
>
0
there is a Riemannian metric
g
on a 3-sphere such that
vol
(
S
3
,
g
)
=
1
and for any map
f
:
S
3
→
R
2
there is some
x
∈
R
2
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diam
(
f
-
1
(
x
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)
>
C
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C
>
0
there is a Riemannian metric
g
on a 3-sphere such that
vol
(
S
3
,
g
)
=
1
and for any map
f
:
S
3
→
R
2
there is some
x
∈
R
2
for which
diam
(
f
-
1
(
x
)
)
>
C
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C
>
0
there is a Riemannian metric
g
on a 3-sphere such that
vol
(
S
3
,
g
)
=
1
and for any map
f
:
S
3
→
R
2
there is some
x
∈
R
2
for which
diam
(
f
-
1
(
x
)
)
>
C
, answering a question of Guth.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00039-020-00533-5</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Geometric and functional analysis, 2020-04, Vol.30 (2), p.574-587 |
| issn | 1016-443X 1420-8970 |
| language | eng |
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| subjects | Analysis Mathematics Mathematics and Statistics |
| title | Uryson Width and Volume |
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