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Mat. Sb., 2003, Volume 194, Number 4, Pages 29–48 (Mi msb726)  

This article is cited in 7 scientific papers (total in 7 papers)

Isoperimetric inequality on conformally hyperbolic manifolds

V. M. Kesel'man

Moscow State Industrial University

Abstract: It is shown that on an arbitrary non-compact Riemannian manifold of conformally hyperbolic type the isoperimetric inequality can be taken by a conformal change of the metric to the same canonical linear form as in the case of the standard hyperbolic Lobachevskii space. Both the absolute isoperimetric inequality and the relative one (for manifolds with boundary) are obtained.
This work develops the results and methods of a joint paper with Zorich, in which the absolute isoperimetric inequality was obtained under a certain additional condition; the resulting statements are definitive in a certain sense.

DOI: https://doi.org/10.4213/sm726

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English version:
Sbornik: Mathematics, 2003, 194:4, 495–513

Bibliographic databases:

UDC: 517.54+514.774
MSC: 53A30, 53C20
Received: 08.04.2002 and 04.02.2003

Citation: V. M. Kesel'man, “Isoperimetric inequality on conformally hyperbolic manifolds”, Mat. Sb., 194:4 (2003), 29–48; Sb. Math., 194:4 (2003), 495–513

Citation in format AMSBIB
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\by V.~M.~Kesel'man
\paper Isoperimetric inequality on conformally
hyperbolic manifolds
\jour Mat. Sb.
\yr 2003
\vol 194
\issue 4
\pages 29--48
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\crossref{https://doi.org/10.4213/sm726}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1991915}
\zmath{https://zbmath.org/?q=an:1075.53027}
\transl
\jour Sb. Math.
\yr 2003
\vol 194
\issue 4
\pages 495--513
\crossref{https://doi.org/10.1070/SM2003v194n04ABEH000726}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0037490939}


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  • https://doi.org/10.4213/sm726
  • http://mi.mathnet.ru/eng/msb/v194/i4/p29

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V.A. Zorich, Publ. Inst. Math. (Belgr.), 75:89 (2004), 25  crossref  mathscinet  zmath
    2. V. M. Kesel'man, “On the isoperimetric inequality on conformally parabolic manifolds”, Russian Math. Surveys, 62:6 (2007), 1210–1211  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. M. Kesel'man, “The isoperimetric inequality on conformally parabolic manifolds”, Sb. Math., 200:1 (2009), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. M. Kesel'man, “The relative isoperimetric inequality on a conformally parabolic manifold with boundary”, Russian Math. Surveys, 65:2 (2010), 384–385  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. A. Zorich, “On the measure of conformal difference between Euclidean and Lobachevsky spaces”, Sb. Math., 202:12 (2011), 1825–1830  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. 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
    7. 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 - 1992–2005 Sbornik: Mathematics (from 1967)
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