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Volume growth and parabolicity |
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| Authors: | Ilkka Holopainen Pekka Koskela |
| Institution: | Department of Mathematics, University of Helsinki, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 Helsinki, Finland ; Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland |
| Abstract: | We characterize |
| Keywords: | Volume growth harmonic function Green's function parabolicity |
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-parabolicity of a noncompact complete Riemannian manifold 
in terms of the volume growth of 
under very weak assumptions on 
. Some of the results also apply to the setting of metric measure spaces.