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Funktsional'nyi Analiz i ego Prilozheniya, 2001, Volume 35, Issue 2, Pages 12–23
DOI: https://doi.org/10.4213/faa242 (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
Full-text PDF (169 kB) Citations (9)
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DOI: https://doi.org/10.4213/faa242
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.
Received: 01.06.2000
English version:
Functional Analysis and Its Applications, 2001, Volume 35, Issue 2, Pages 90–99
DOI: https://doi.org/10.1023/A:1017523114581
Bibliographic databases:
Document Type: Article
UDC: 517.54+514.774
Language: Russian
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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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