Ukrainian Mathematical Bulletin

Volume 1, Issue 2, 2004 pp. 237-250.

Harmonic Functions of Prescribed Growth on Quasimodel Riemannian Manifolds

Authors: A.G.Losev
Author institution: Department of Mathematics, Volgograd State University, Russia

Summary: We study the asymptotic behavior of solutions of the Laplace-- Beltrami weight equation on noncompact Riemannian manifolds generalizing both model manifolds and warped Riemannian products. On the basis of the spectral properties of the analyzed manifolds, we estimate the dimensionalities of the spaces of harmonic functions of prescribed growth in terms of the internal characteristics of these manifolds.

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