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Sbornik: Mathematics, 2011, Volume 202, Issue 7, Pages 1043–1058
DOI: https://doi.org/10.1070/SM2011v202n07ABEH004176 (Mi sm7738) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The relative isoperimetric inequality on a conformally parabolic manifold with boundary

V. M. Kesel'man

Moscow State Industrial University
English version PDF (316 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2011v202n07ABEH004176
Abstract: For an arbitrary noncompact $n$-dimensional Riemannian manifold with a boundary of conformally parabolic type it is proved that there exists a conformal change of metric such that a relative isoperimetric inequality of the same form as in the closed $n$-dimensional Euclidean half-space holds on the manifold with the new metric. This isoperimetric inequality is asymptotically sharp.
Bibliography: 6 titles.
Keywords: Riemannian manifold, conformal type of a manifold, conformal capacity, conformal metrics, isoperimetric function.
Received: 17.05.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 7, Pages 117–134
DOI: https://doi.org/10.4213/sm7738
Bibliographic databases:
Document Type: Article
UDC: 517.54+514.774
MSC: Primary 53A30, 53C20; Secondary 31C45
Language: English
Original paper language: Russian
Citation: V. M. Kesel'man, “The relative isoperimetric inequality on a conformally parabolic manifold with boundary”, Mat. Sb., 202:7 (2011), 117–134; Sb. Math., 202:7 (2011), 1043–1058
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2011v202n07ABEH004176
  • https://www.mathnet.ru/eng/sm/v202/i7/p117
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    This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:559
    Russian version PDF:199
    English version PDF:12
    References:82
    First page:22
     
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