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On a criterion of conformal parabolicity of a Riemannian manifold. (English. Russian original) Zbl 1326.53045
Sb. Math. 206, No. 3, 389-420 (2015); translation from Mat. Sb. 206, No. 3, 57-90 (2015).
Author’s 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.
53C20 Global Riemannian geometry, including pinching
53A30 Conformal differential geometry (MSC2010)
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