Pyramid Ricci flow in higher dimensions
In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold ( M n , g 0 ) that is PIC1, or more generally satisfies a lower curvature bound K IC 1 ≥ - α 0 . That is, instead of constructing a flow on M × [ 0 , T ] , we construct it on a subset of space-time that is...
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| Veröffentlicht in: | Mathematische Zeitschrift 2020-10, Vol.296 (1-2), p.511-523 |
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| container_title | Mathematische Zeitschrift |
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| creator | McLeod, Andrew D. Topping, Peter M. |
| description | In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold
(
M
n
,
g
0
)
that is PIC1, or more generally satisfies a lower curvature bound
K
IC
1
≥
-
α
0
. That is, instead of constructing a flow on
M
×
[
0
,
T
]
, we construct it on a subset of space-time that is a union of parabolic cylinders
B
g
0
(
x
0
,
k
)
×
[
0
,
T
k
]
for each
k
∈
N
, where
T
k
↓
0
, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed
IC
1
-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder. |
| doi_str_mv | 10.1007/s00209-020-02472-1 |
| format | Article |
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(
M
n
,
g
0
)
that is PIC1, or more generally satisfies a lower curvature bound
K
IC
1
≥
-
α
0
. That is, instead of constructing a flow on
M
×
[
0
,
T
]
, we construct it on a subset of space-time that is a union of parabolic cylinders
B
g
0
(
x
0
,
k
)
×
[
0
,
T
k
]
for each
k
∈
N
, where
T
k
↓
0
, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed
IC
1
-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-020-02472-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Curvature ; Mathematics ; Mathematics and Statistics ; Riemann manifold</subject><ispartof>Mathematische Zeitschrift, 2020-10, Vol.296 (1-2), p.511-523</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-5d0beba97ba44a99b1beaeda3514a4ea9f162ccc73899ecd815f974d7193bfe13</citedby><cites>FETCH-LOGICAL-c363t-5d0beba97ba44a99b1beaeda3514a4ea9f162ccc73899ecd815f974d7193bfe13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00209-020-02472-1$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00209-020-02472-1$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>McLeod, Andrew D.</creatorcontrib><creatorcontrib>Topping, Peter M.</creatorcontrib><title>Pyramid Ricci flow in higher dimensions</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold
(
M
n
,
g
0
)
that is PIC1, or more generally satisfies a lower curvature bound
K
IC
1
≥
-
α
0
. That is, instead of constructing a flow on
M
×
[
0
,
T
]
, we construct it on a subset of space-time that is a union of parabolic cylinders
B
g
0
(
x
0
,
k
)
×
[
0
,
T
k
]
for each
k
∈
N
, where
T
k
↓
0
, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed
IC
1
-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder.</description><subject>Curvature</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Riemann manifold</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9UE1LxDAQDaJgXf0DngoePEUzSdo0R1n8ggVF9BySNNnNsm3XZBfZf29qBW8e5s3Ae_NmeAhdArkBQsRtIoQSiTPk4oJiOEIFcJaHhrJjVGS-wlUj-Ck6S2lNSCYFL9D16yHqLrTlW7A2lH4zfJWhL1dhuXKxbEPn-hSGPp2jE683yV389hn6eLh_nz_hxcvj8_xugS2r2Q5XLTHOaCmM5lxLacA47VrNKuCaOy091NRaK1gjpbNtA5WXgrcCJDPeAZuhq8l3G4fPvUs7tR72sc8nFR0_Bl4LklV0Utk4pBSdV9sYOh0PCogaA1FTICqD-glEjdZsWkpZ3C9d_LP-Z-sbEVhiUA</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>McLeod, Andrew D.</creator><creator>Topping, Peter M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201001</creationdate><title>Pyramid Ricci flow in higher dimensions</title><author>McLeod, Andrew D. ; Topping, Peter M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-5d0beba97ba44a99b1beaeda3514a4ea9f162ccc73899ecd815f974d7193bfe13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Curvature</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Riemann manifold</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>McLeod, Andrew D.</creatorcontrib><creatorcontrib>Topping, Peter M.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>McLeod, Andrew D.</au><au>Topping, Peter M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pyramid Ricci flow in higher dimensions</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>296</volume><issue>1-2</issue><spage>511</spage><epage>523</epage><pages>511-523</pages><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold
(
M
n
,
g
0
)
that is PIC1, or more generally satisfies a lower curvature bound
K
IC
1
≥
-
α
0
. That is, instead of constructing a flow on
M
×
[
0
,
T
]
, we construct it on a subset of space-time that is a union of parabolic cylinders
B
g
0
(
x
0
,
k
)
×
[
0
,
T
k
]
for each
k
∈
N
, where
T
k
↓
0
, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed
IC
1
-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-020-02472-1</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5874 |
| ispartof | Mathematische Zeitschrift, 2020-10, Vol.296 (1-2), p.511-523 |
| issn | 0025-5874 1432-1823 |
| language | eng |
| recordid | cdi_proquest_journals_2437414670 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Curvature Mathematics Mathematics and Statistics Riemann manifold |
| title | Pyramid Ricci flow in higher dimensions |
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