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Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 2, Pages 12–23 (Mi faa242)  

This article is cited in 9 scientific papers (total in 9 papers)

The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type

V. A. Zoricha, V. M. Kesel'manb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow State Industrial University

Abstract: We prove that the maximal isoperimetric function on a Riemannian manifold of conformally hyperbolic type can be reduced to the linear canonical form $P(x)=x$ by a conformal change of the Riemannian metric. In other words, the isoperimetric inequality $P(V(D))\le S(\partial D)$, relating the volume $V(D)$ of a domain $D$ to the area $S(\partial D)$ of its boundary, can be reduced to the form $V(D)\le S(\partial D)$, known for the Lobachevskii hyperbolic space.

DOI: https://doi.org/10.4213/faa242

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English version:
Functional Analysis and Its Applications, 2001, 35:2, 90–99

Bibliographic databases:

UDC: 517.54+514.774
Received: 01.06.2000

Citation: V. A. Zorich, V. M. Kesel'man, “The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 12–23; Funct. Anal. Appl., 35:2 (2001), 90–99

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. A. Zorich, V. M. Kesel'man, “Fundamental frequency and conformal type of a Riemannian manifold”, Russian Math. Surveys, 57:2 (2002), 428–429  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Zorich, “Quasi-conformal maps and the asymptotic geometry of manifolds”, Russian Math. Surveys, 57:3 (2002), 437–462  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. M. Kesel'man, “Isoperimetric inequality on conformally hyperbolic manifolds”, Sb. Math., 194:4 (2003), 495–513  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. 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
    5. 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
    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
    8. V. A. Zorich, “Some observations concerning multidimensional quasiconformal mappings”, Sb. Math., 208:3 (2017), 377–398  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. V. A. Zorich, “On a question of Gromov concerning the generalized Liouville theorem”, Russian Math. Surveys, 74:1 (2019), 175–177  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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