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Mat. Sb., 2011, Volume 202, Number 7, Pages 117–134 (Mi msb7738)  

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

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.

DOI: https://doi.org/10.4213/sm7738

Full text: PDF file (542 kB)
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English version:
Sbornik: Mathematics, 2011, 202:7, 1043–1058

Bibliographic databases:

UDC: 517.54+514.774
MSC: Primary 53A30, 53C20; Secondary 31C45
Received: 17.05.2010

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/10.4213/sm7738
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Keselman V.M., “Evklidovo izoperimetricheskoe neravenstvo v klasse konformnykh metrik nekompaktnogo rimanova mnogoobraziya”, Vestn. Volgogradskogo gos. un-ta. Ser. 1. Matem. Fiz., 2011, no. 2, 33–42  elib
    2. Keselman V.M., “Evklidovo izoperimetricheskoe neravenstvo v klasse konformnykh metrik nekompaktnogo rimanova mnogoobraziya”, Vestnik volgogradskogo gosudarstvennogo universiteta. seriya 1: matematika. fizika, 2011, no. 2, 33–42  elib
    3. V. M. Keselman, “On a criterion of conformal parabolicity of a Riemannian manifold”, Sb. Math., 206:3 (2015), 389–420  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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