Area spaces: First steps

Dmitri Burago; Sergei Ivanov

doi:10.1007/s00039-009-0018-2

Area spaces: First steps

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the "lcycles") equipped with the filling area distance, and discuss possible approaches to "spaces with area structures".

Original language	English (US)
Pages (from-to)	662-677
Number of pages	16
Journal	Geometric and Functional Analysis
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s00039-009-0018-2
State	Published - 2009

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-009-0018-2

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@article{17b5c699c88645b59a46a2134c61eb02,

title = "Area spaces: First steps",

abstract = "We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the {"}lcycles{"}) equipped with the filling area distance, and discuss possible approaches to {"}spaces with area structures{"}.",

author = "Dmitri Burago and Sergei Ivanov",

note = "Funding Information: Keywords and phrases: Riemannian metric, integral current, filling area, flat norm, area space 2000 Mathematics Subject Classification: 53C65, 49Q15 The first author is partially supported by the NSF Grant DMS-0412166. The second author is partially supported by the Dynasty foundation and RFBR grant 08-01-00079-a.",

year = "2009",

doi = "10.1007/s00039-009-0018-2",

language = "English (US)",

volume = "19",

pages = "662--677",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Area spaces

T2 - First steps

AU - Burago, Dmitri

AU - Ivanov, Sergei

N1 - Funding Information: Keywords and phrases: Riemannian metric, integral current, filling area, flat norm, area space 2000 Mathematics Subject Classification: 53C65, 49Q15 The first author is partially supported by the NSF Grant DMS-0412166. The second author is partially supported by the Dynasty foundation and RFBR grant 08-01-00079-a.

PY - 2009

Y1 - 2009

N2 - We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the "lcycles") equipped with the filling area distance, and discuss possible approaches to "spaces with area structures".

AB - We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the "lcycles") equipped with the filling area distance, and discuss possible approaches to "spaces with area structures".

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U2 - 10.1007/s00039-009-0018-2

DO - 10.1007/s00039-009-0018-2

M3 - Article

AN - SCOPUS:84904989014

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VL - 19

SP - 662

EP - 677

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Area spaces: First steps

Abstract

All Science Journal Classification (ASJC) codes

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