On a criterion of conformal parabolicity of a Riemannian manifold. (English. Russian original) Zbl 1326.53045

Kesel’man, V. M.

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.

Reviewer: Witold Mozgawa (Lublin)

MSC:

53C20	Global Riemannian geometry, including pinching
53A30	Conformal differential geometry (MSC2010)

Keywords:

Riemannian manifold; conformal metric; conformal capacity; conformal type of a manifold; isoperimetric function of a Riemannian manifold