Geodesic
The relative isoperimetric inequality on a conformally parabolic manifold with boundary
Sbornik. Mathematics, Tome 202 (2011) no. 7, pp. 1043-1058 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary noncompact $n$-dimensional Riemannian manifold with a boundary of conformally parabolic type it is proved that there exists a conformal change of metric such that a relative isoperimetric inequality of the same form as in the closed $n$-dimensional Euclidean half-space holds on the manifold with the new metric. This isoperimetric inequality is asymptotically sharp. Bibliography: 6 titles.
Keywords: Riemannian manifold, conformal type of a manifold, conformal capacity, conformal metrics, isoperimetric function. 
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V. M. Kesel'man. The relative isoperimetric inequality on a conformally parabolic manifold with boundary. Sbornik. Mathematics, Tome 202 (2011) no. 7, pp. 1043-1058. http://geodesic.mathdoc.fr/item/SM_2011_202_7_a4/

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