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dc.contributor.author
Kleiner, Bruce
dc.contributor.author
Lang, Urs
dc.date.accessioned
2020-08-06T07:53:20Z
dc.date.available
2020-03-12T02:23:06Z
dc.date.available
2020-03-12T09:59:44Z
dc.date.available
2020-08-06T07:53:20Z
dc.date.issued
2020-08
dc.identifier.issn
0020-9910
dc.identifier.issn
1432-1297
dc.identifier.other
10.1007/s00222-020-00955-w
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/404450
dc.description.abstract
The large-scale geometry of hyperbolic metric spaces exhibits many distinctive features, such as the stability of quasi-geodesics (the Morse Lemma), the visibility property, and the homeomorphism between visual boundaries induced by a quasi-isometry. We prove a number of closely analogous results for spaces of rank n≥ 2 in an asymptotic sense, under some weak assumptions reminiscent of nonpositive curvature. For this purpose we replace quasi-geodesic lines with quasi-minimizing (locally finite) n-cycles of rn volume growth; prime examples include n-cycles associated with n-quasiflats. Solving an asymptotic Plateau problem and producing unique tangent cones at infinity for such cycles, we show in particular that every quasi-isometry between two proper CAT (0) spaces of asymptotic rank n extends to a class of (n- 1) -cycles in the Tits boundaries.
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.title
Higher rank hyperbolicity
en_US
dc.type
Journal Article
dc.date.published
2020-02-18
ethz.journal.title
Inventiones mathematicae
ethz.journal.volume
221
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Invent. math.
ethz.pages.start
597
en_US
ethz.pages.end
664
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03500 - Lang, Urs / Lang, Urs
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03500 - Lang, Urs / Lang, Urs
ethz.relation.isNewVersionOf
20.500.11850/315942
ethz.date.deposited
2020-03-12T02:23:15Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-08-06T07:53:37Z
ethz.rosetta.lastUpdated
2023-02-06T20:16:12Z
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true
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