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Sbornik: Mathematics, 2009, Volume 200, Issue 1, Pages 1–33
DOI: https://doi.org/10.1070/SM2009v200n01ABEH003985 (Mi sm6379) 		 
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
English version PDF (438 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2009v200n01ABEH003985
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.
Received: 09.06.2008 and 22.09.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 1, Pages 3–36
DOI: https://doi.org/10.4213/sm6379
Bibliographic databases:
UDC: 517.54+514.774
MSC: Primary 53A30, 53C20; Secondary 31C45
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:624
    Russian version PDF:224
    English version PDF:18
    References:61
    First page:9
     
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