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Mat. Sb., 2009, Volume 200, Number 1, Pages 3–36 (Mi msb6379)  

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

The isoperimetric inequality on conformally parabolic manifolds

V. M. Kesel'man

Moscow State Industrial University

Abstract: For non-compact Riemannian manifolds without boundary the following conjecture is proved: on a Riemannian manifold of conformally parabolic type, after a conformal change of the metric the isoperimetric function (responsible for the isoperimetric inequality) can be transformed into the same form as in the case of the Euclidean space of the corresponding dimension.
Bibliography: 8 titles.

Keywords: Riemannian manifold, conformal type of a manifold, conformal metrics, conformal capacity, isoperimetric function.

DOI: https://doi.org/10.4213/sm6379

Full text: PDF file (679 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:1, 1–33

Bibliographic databases:

UDC: 517.54+514.774
MSC: Primary 53A30, 53C20; Secondary 31C45
Received: 09.06.2008 and 22.09.2008

Citation: V. M. Kesel'man, “The isoperimetric inequality on conformally parabolic manifolds”, Mat. Sb., 200:1 (2009), 3–36; Sb. Math., 200:1 (2009), 1–33

Citation in format AMSBIB
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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. 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
    2. 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
    3. 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
    4. 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
    5. V. M. Kesel'man, “The relative isoperimetric inequality on a conformally parabolic manifold with boundary”, Sb. Math., 202:7 (2011), 1043–1058  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. 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
    7. V. A. Zorich, “Some observations concerning multidimensional quasiconformal mappings”, Sb. Math., 208:3 (2017), 377–398  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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