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Mat. Sb., 2015, Volume 206, Number 3, Pages 57–90 (Mi msb8290)  

This article is cited in 1 scientific paper (total in 1 paper)

On a criterion of conformal parabolicity of a Riemannian manifold

V. M. Keselman

Moscow State Industrial University

Abstract: The paper relates to the circle of problems concerning the connection between the conformal type of a Riemannian manifold and the canonical form of its isoperimetric function. Two special examples of 2-manifolds are constructed, which explain the meaning, role and importance of the conditions involved in the criterion, previously obtained by the author, which decides whether a noncompact Riemannian $n$-manifold is conformally parabolic.
Bibliography: 8 titles.

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

DOI: https://doi.org/10.4213/sm8290

Full text: PDF file (700 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:3, 389–420

Bibliographic databases:

UDC: 517.54+514.774
MSC: 53A30, 53C20
Received: 11.10.2013

Citation: V. M. Keselman, “On a criterion of conformal parabolicity of a Riemannian manifold”, Mat. Sb., 206:3 (2015), 57–90; Sb. Math., 206:3 (2015), 389–420

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v206/i3/p57

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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, “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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